Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.6% → 92.9%

Time: 21.3s

Alternatives: 23

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.6% 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: 92.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

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 -2e-294)
     (fma (/ (- y z) (- a z)) (- t x) x)
     (if (<= t_2 0.0) (+ t (* x (/ (- y 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 <= -2e-294) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - 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 <= -2e-294)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - 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, -2e-294], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000003e-294

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. distribute-rgt-in 74.7%

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

      3. *-lft-identity 74.7%

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

      4. mul-1-neg 74.7%

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

      5. distribute-neg-frac 74.7%

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

      6. associate-*l/ 71.7%

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

      7. neg-mul-1 71.7%

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

      8. associate-*r* 71.7%

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

      9. *-commutative 71.7%

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

      10. associate-*r/ 71.7%

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

      11. +-commutative 71.7%

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

      12. associate-+l+ 69.8%

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

   5. Simplified 94.4%

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

   if -2.00000000000000003e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   3. Taylor expanded in z around inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. distribute-lft-out-- 90.9%

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

      3. div-sub 90.9%

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

      4. mul-1-neg 90.9%

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

      5. unsub-neg 90.9%

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

      6. distribute-rgt-out-- 90.9%

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

      7. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in t around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. associate-*r/ 95.5%

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

      3. *-commutative 95.5%

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

      4. distribute-rgt-neg-in 95.5%

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

   8. Simplified 95.5%

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

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

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. fma-def 95.2%

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

   3. Simplified 95.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-196} \lor \neg \left(t_2 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (or (<= t_2 -2e-196) (not (<= t_2 0.0)))
     (fma (- y z) t_1 x)
     (- t (/ (- t x) (/ z (- y a)))))))

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 <= -2e-196) || !(t_2 <= 0.0)) {
		tmp = fma((y - z), t_1, x);
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	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 <= -2e-196) || !(t_2 <= 0.0))
		tmp = fma(Float64(y - z), t_1, x);
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	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[Or[LessEqual[t$95$2, -2e-196], N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(t - N[(N[(t - x), $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)))) < -2.0000000000000001e-196 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 93.6%

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

   3. Simplified 93.6%

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

   if -2.0000000000000001e-196 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.6%

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

   3. Taylor expanded in z around inf 89.5%

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

      1. associate--l+ 89.5%

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

      2. distribute-lft-out-- 89.5%

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

      3. div-sub 89.5%

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

      4. mul-1-neg 89.5%

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

      5. unsub-neg 89.5%

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

      6. distribute-rgt-out-- 89.4%

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

      7. associate-/l* 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-196} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-196} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-196) (not (<= t_1 0.0)))
     t_1
     (- t (/ (- t x) (/ 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 <= -2e-196) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (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 <= (-2d-196)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (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 <= -2e-196) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (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 <= -2e-196) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) / (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 <= -2e-196) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / 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 <= -2e-196) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) / (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, -2e-196], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $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)))) < -2.0000000000000001e-196 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

   if -2.0000000000000001e-196 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.6%

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

   3. Taylor expanded in z around inf 89.5%

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

      1. associate--l+ 89.5%

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

      2. distribute-lft-out-- 89.5%

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

      3. div-sub 89.5%

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

      4. mul-1-neg 89.5%

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

      5. unsub-neg 89.5%

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

      6. distribute-rgt-out-- 89.4%

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

      7. associate-/l* 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-196} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -250000000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -62:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq -0.72:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-73} \lor \neg \left(z \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))))
   (if (<= z -9.6e+83)
     t_1
     (if (<= z -2.05e+21)
       (- x (/ x (/ a y)))
       (if (<= z -250000000000.0)
         (- t (* y (/ t z)))
         (if (<= z -62.0)
           (/ t (/ (- a z) y))
           (if (<= z -0.72)
             (/ (- t) (+ (/ a z) -1.0))
             (if (or (<= z -8e-73) (not (<= z 1.3e-9)))
               t_1
               (+ x (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -9.6e+83) {
		tmp = t_1;
	} else if (z <= -2.05e+21) {
		tmp = x - (x / (a / y));
	} else if (z <= -250000000000.0) {
		tmp = t - (y * (t / z));
	} else if (z <= -62.0) {
		tmp = t / ((a - z) / y);
	} else if (z <= -0.72) {
		tmp = -t / ((a / z) + -1.0);
	} else if ((z <= -8e-73) || !(z <= 1.3e-9)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (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 = t + (x * (y / z))
    if (z <= (-9.6d+83)) then
        tmp = t_1
    else if (z <= (-2.05d+21)) then
        tmp = x - (x / (a / y))
    else if (z <= (-250000000000.0d0)) then
        tmp = t - (y * (t / z))
    else if (z <= (-62.0d0)) then
        tmp = t / ((a - z) / y)
    else if (z <= (-0.72d0)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if ((z <= (-8d-73)) .or. (.not. (z <= 1.3d-9))) then
        tmp = t_1
    else
        tmp = x + (t * (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 = t + (x * (y / z));
	double tmp;
	if (z <= -9.6e+83) {
		tmp = t_1;
	} else if (z <= -2.05e+21) {
		tmp = x - (x / (a / y));
	} else if (z <= -250000000000.0) {
		tmp = t - (y * (t / z));
	} else if (z <= -62.0) {
		tmp = t / ((a - z) / y);
	} else if (z <= -0.72) {
		tmp = -t / ((a / z) + -1.0);
	} else if ((z <= -8e-73) || !(z <= 1.3e-9)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	tmp = 0
	if z <= -9.6e+83:
		tmp = t_1
	elif z <= -2.05e+21:
		tmp = x - (x / (a / y))
	elif z <= -250000000000.0:
		tmp = t - (y * (t / z))
	elif z <= -62.0:
		tmp = t / ((a - z) / y)
	elif z <= -0.72:
		tmp = -t / ((a / z) + -1.0)
	elif (z <= -8e-73) or not (z <= 1.3e-9):
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -9.6e+83)
		tmp = t_1;
	elseif (z <= -2.05e+21)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= -250000000000.0)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= -62.0)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	elseif (z <= -0.72)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif ((z <= -8e-73) || !(z <= 1.3e-9))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -9.6e+83)
		tmp = t_1;
	elseif (z <= -2.05e+21)
		tmp = x - (x / (a / y));
	elseif (z <= -250000000000.0)
		tmp = t - (y * (t / z));
	elseif (z <= -62.0)
		tmp = t / ((a - z) / y);
	elseif (z <= -0.72)
		tmp = -t / ((a / z) + -1.0);
	elseif ((z <= -8e-73) || ~((z <= 1.3e-9)))
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+83], t$95$1, If[LessEqual[z, -2.05e+21], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -250000000000.0], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -62.0], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.72], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8e-73], N[Not[LessEqual[z, 1.3e-9]], $MachinePrecision]], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -9.59999999999999965e83 or -0.71999999999999997 < z < -7.99999999999999998e-73 or 1.3000000000000001e-9 < z

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

      6. distribute-rgt-out-- 67.5%

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

      7. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around inf 71.5%

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

   7. Taylor expanded in t around 0 58.4%

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

      1. associate-*r/ 64.0%

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

      2. neg-mul-1 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-neg-frac 64.0%

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

   9. Simplified 64.0%

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

   if -9.59999999999999965e83 < z < -2.05e21

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

      3. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

   if -2.05e21 < z < -2.5e11

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. distribute-lft-out-- 50.5%

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

      3. div-sub 50.5%

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

      4. mul-1-neg 50.5%

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

      5. unsub-neg 50.5%

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

      6. distribute-rgt-out-- 50.5%

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

      7. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in y around inf 70.3%

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

   7. Taylor expanded in t around inf 45.3%

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

      1. associate-*l/ 70.3%

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

      2. *-commutative 70.3%

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

   9. Simplified 70.3%

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

   if -2.5e11 < z < -62

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 68.6%

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

   4. Taylor expanded in y around inf 68.6%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -62 < z < -0.71999999999999997

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. sub-neg 100.0%

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

      5. *-inverses 100.0%

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

      6. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   if -7.99999999999999998e-73 < z < 1.3000000000000001e-9

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around inf 66.3%

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

      1. associate-*r/ 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -250000000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -62:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq -0.72:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-73} \lor \neg \left(z \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.00155:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -6.5e+106)
     t
     (if (<= z -8e+19)
       x
       (if (<= z -0.00155)
         t_1
         (if (<= z -4.5e-193)
           x
           (if (<= z 6.3e-178)
             t_1
             (if (<= z 1.25e-36) x (if (<= z 2.5e-13) (/ t (/ a y)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -6.5e+106) {
		tmp = t;
	} else if (z <= -8e+19) {
		tmp = x;
	} else if (z <= -0.00155) {
		tmp = t_1;
	} else if (z <= -4.5e-193) {
		tmp = x;
	} else if (z <= 6.3e-178) {
		tmp = t_1;
	} else if (z <= 1.25e-36) {
		tmp = x;
	} else if (z <= 2.5e-13) {
		tmp = t / (a / y);
	} 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 = t * (y / (a - z))
    if (z <= (-6.5d+106)) then
        tmp = t
    else if (z <= (-8d+19)) then
        tmp = x
    else if (z <= (-0.00155d0)) then
        tmp = t_1
    else if (z <= (-4.5d-193)) then
        tmp = x
    else if (z <= 6.3d-178) then
        tmp = t_1
    else if (z <= 1.25d-36) then
        tmp = x
    else if (z <= 2.5d-13) then
        tmp = t / (a / y)
    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 = t * (y / (a - z));
	double tmp;
	if (z <= -6.5e+106) {
		tmp = t;
	} else if (z <= -8e+19) {
		tmp = x;
	} else if (z <= -0.00155) {
		tmp = t_1;
	} else if (z <= -4.5e-193) {
		tmp = x;
	} else if (z <= 6.3e-178) {
		tmp = t_1;
	} else if (z <= 1.25e-36) {
		tmp = x;
	} else if (z <= 2.5e-13) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -6.5e+106:
		tmp = t
	elif z <= -8e+19:
		tmp = x
	elif z <= -0.00155:
		tmp = t_1
	elif z <= -4.5e-193:
		tmp = x
	elif z <= 6.3e-178:
		tmp = t_1
	elif z <= 1.25e-36:
		tmp = x
	elif z <= 2.5e-13:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.5e+106)
		tmp = t;
	elseif (z <= -8e+19)
		tmp = x;
	elseif (z <= -0.00155)
		tmp = t_1;
	elseif (z <= -4.5e-193)
		tmp = x;
	elseif (z <= 6.3e-178)
		tmp = t_1;
	elseif (z <= 1.25e-36)
		tmp = x;
	elseif (z <= 2.5e-13)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -6.5e+106)
		tmp = t;
	elseif (z <= -8e+19)
		tmp = x;
	elseif (z <= -0.00155)
		tmp = t_1;
	elseif (z <= -4.5e-193)
		tmp = x;
	elseif (z <= 6.3e-178)
		tmp = t_1;
	elseif (z <= 1.25e-36)
		tmp = x;
	elseif (z <= 2.5e-13)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+106], t, If[LessEqual[z, -8e+19], x, If[LessEqual[z, -0.00155], t$95$1, If[LessEqual[z, -4.5e-193], x, If[LessEqual[z, 6.3e-178], t$95$1, If[LessEqual[z, 1.25e-36], x, If[LessEqual[z, 2.5e-13], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5000000000000003e106 or 2.49999999999999995e-13 < z

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -6.5000000000000003e106 < z < -8e19 or -0.00154999999999999995 < z < -4.4999999999999999e-193 or 6.3e-178 < z < 1.25000000000000001e-36

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 39.2%

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

   if -8e19 < z < -0.00154999999999999995 or -4.4999999999999999e-193 < z < 6.3e-178

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 58.4%

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

   4. Taylor expanded in y around inf 50.0%

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

      1. expm1-log1p-u 17.5%

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

      2. expm1-udef 12.8%

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

      3. associate-/l* 16.9%

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

   6. Applied egg-rr 16.9%

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

      1. expm1-def 20.1%

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

      2. expm1-log1p 52.8%

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

      3. associate-/l* 50.0%

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

      4. associate-*r/ 52.7%

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

   8. Simplified 52.7%

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

   if 1.25000000000000001e-36 < z < 2.49999999999999995e-13

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 67.9%

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

   4. Taylor expanded in a around inf 68.6%

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

      1. associate-/l* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in y around inf 99.5%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.00155:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+22}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-73} \lor \neg \left(z \leq 6.6 \cdot 10^{-19}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- t x) (/ z (- y a))))))
   (if (<= z -8.8e+83)
     t_1
     (if (<= z -6e+22)
       (+ x (* (- t x) (/ y a)))
       (if (or (<= z -1.2e-73) (not (<= z 6.6e-19)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -6e+22) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -1.2e-73) || !(z <= 6.6e-19)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - ((t - x) / (z / (y - a)))
    if (z <= (-8.8d+83)) then
        tmp = t_1
    else if (z <= (-6d+22)) then
        tmp = x + ((t - x) * (y / a))
    else if ((z <= (-1.2d-73)) .or. (.not. (z <= 6.6d-19))) then
        tmp = t_1
    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 t_1 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -6e+22) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -1.2e-73) || !(z <= 6.6e-19)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) / (z / (y - a)))
	tmp = 0
	if z <= -8.8e+83:
		tmp = t_1
	elif z <= -6e+22:
		tmp = x + ((t - x) * (y / a))
	elif (z <= -1.2e-73) or not (z <= 6.6e-19):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -6e+22)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif ((z <= -1.2e-73) || !(z <= 6.6e-19))
		tmp = t_1;
	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)
	t_1 = t - ((t - x) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -6e+22)
		tmp = x + ((t - x) * (y / a));
	elseif ((z <= -1.2e-73) || ~((z <= 6.6e-19)))
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+83], t$95$1, If[LessEqual[z, -6e+22], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.2e-73], N[Not[LessEqual[z, 6.6e-19]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999995e83 or -6e22 < z < -1.20000000000000003e-73 or 6.5999999999999995e-19 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. distribute-lft-out-- 66.7%

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

      3. div-sub 66.7%

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

      4. mul-1-neg 66.7%

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

      5. unsub-neg 66.7%

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

      6. distribute-rgt-out-- 66.8%

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

      7. associate-/l* 80.3%

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

   5. Simplified 80.3%

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

   if -8.79999999999999995e83 < z < -6e22

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. associate-/l* 78.9%

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

      2. associate-/r/ 78.9%

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

   5. Simplified 78.9%

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

   if -1.20000000000000003e-73 < z < 6.5999999999999995e-19

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.5%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+22}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-73} \lor \neg \left(z \leq 6.6 \cdot 10^{-19}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-38}:\\ \;\;\;\;\frac{-a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -2.1e+72)
     t
     (if (<= z -2.6e-19)
       t_1
       (if (<= z -1e-38)
         (/ (- a) (/ z x))
         (if (<= z -1.55e-192) x (if (<= z 22.0) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.1e+72) {
		tmp = t;
	} else if (z <= -2.6e-19) {
		tmp = t_1;
	} else if (z <= -1e-38) {
		tmp = -a / (z / x);
	} else if (z <= -1.55e-192) {
		tmp = x;
	} else if (z <= 22.0) {
		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 = t * ((y - z) / a)
    if (z <= (-2.1d+72)) then
        tmp = t
    else if (z <= (-2.6d-19)) then
        tmp = t_1
    else if (z <= (-1d-38)) then
        tmp = -a / (z / x)
    else if (z <= (-1.55d-192)) then
        tmp = x
    else if (z <= 22.0d0) 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 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.1e+72) {
		tmp = t;
	} else if (z <= -2.6e-19) {
		tmp = t_1;
	} else if (z <= -1e-38) {
		tmp = -a / (z / x);
	} else if (z <= -1.55e-192) {
		tmp = x;
	} else if (z <= 22.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -2.1e+72:
		tmp = t
	elif z <= -2.6e-19:
		tmp = t_1
	elif z <= -1e-38:
		tmp = -a / (z / x)
	elif z <= -1.55e-192:
		tmp = x
	elif z <= 22.0:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -2.1e+72)
		tmp = t;
	elseif (z <= -2.6e-19)
		tmp = t_1;
	elseif (z <= -1e-38)
		tmp = Float64(Float64(-a) / Float64(z / x));
	elseif (z <= -1.55e-192)
		tmp = x;
	elseif (z <= 22.0)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -2.1e+72)
		tmp = t;
	elseif (z <= -2.6e-19)
		tmp = t_1;
	elseif (z <= -1e-38)
		tmp = -a / (z / x);
	elseif (z <= -1.55e-192)
		tmp = x;
	elseif (z <= 22.0)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+72], t, If[LessEqual[z, -2.6e-19], t$95$1, If[LessEqual[z, -1e-38], N[((-a) / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-192], x, If[LessEqual[z, 22.0], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1000000000000001e72 or 22 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 51.1%

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

   if -2.1000000000000001e72 < z < -2.60000000000000013e-19 or -1.55e-192 < z < 22

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 52.1%

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

   4. Taylor expanded in a around inf 45.7%

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

      1. associate-/l* 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in t around 0 45.7%

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

      1. associate-*r/ 48.0%

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

   9. Simplified 48.0%

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

   if -2.60000000000000013e-19 < z < -9.9999999999999996e-39

   1. Initial program 3.1%

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

   3. Taylor expanded in y around 0 3.1%

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

      1. mul-1-neg 3.1%

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

      2. unsub-neg 3.1%

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

      3. associate-/l* 4.5%

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

      4. associate-/r/ 3.1%

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

   5. Simplified 3.1%

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

   6. Taylor expanded in t around 0 3.1%

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

      1. sub-neg 3.1%

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

      2. mul-1-neg 3.1%

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

      3. remove-double-neg 3.1%

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

      4. associate-/l* 3.1%

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

      5. div-sub 3.1%

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

      6. sub-neg 3.1%

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

      7. *-inverses 3.1%

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

      8. metadata-eval 3.1%

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

   8. Simplified 3.1%

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

   9. Taylor expanded in a around 0 3.1%

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

       1. neg-mul-1 3.1%

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

       2. associate-+r+ 76.2%

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

       3. neg-mul-1 76.2%

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

       4. mul-1-neg 76.2%

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

       5. unsub-neg 76.2%

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

       6. distribute-rgt1-in 76.2%

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

       7. metadata-eval 76.2%

          \[\leadsto \color{blue}{0} \cdot x - \frac{a \cdot x}{z} \]

       8. mul0-lft 76.2%

          \[\leadsto \color{blue}{0} - \frac{a \cdot x}{z} \]

       9. neg-sub0 76.2%

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

       10. associate-/l* 76.2%

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

       11. distribute-neg-frac 76.2%

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

   11. Simplified 76.2%

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

   if -9.9999999999999996e-39 < z < -1.55e-192

   1. Initial program 88.3%

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

   3. Taylor expanded in a around inf 49.7%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-38}:\\ \;\;\;\;\frac{-a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+16}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-73} \lor \neg \left(z \leq 1.65 \cdot 10^{-18}\right):\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+83)
   (+ t (* x (/ y z)))
   (if (<= z -1e+16)
     (+ x (* (- t x) (/ y a)))
     (if (or (<= z -2.2e-73) (not (<= z 1.65e-18)))
       (- t (/ (* y (- t x)) z))
       (+ x (/ y (/ a (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t + (x * (y / z));
	} else if (z <= -1e+16) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -2.2e-73) || !(z <= 1.65e-18)) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+83)) then
        tmp = t + (x * (y / z))
    else if (z <= (-1d+16)) then
        tmp = x + ((t - x) * (y / a))
    else if ((z <= (-2.2d-73)) .or. (.not. (z <= 1.65d-18))) then
        tmp = t - ((y * (t - x)) / z)
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t + (x * (y / z));
	} else if (z <= -1e+16) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -2.2e-73) || !(z <= 1.65e-18)) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+83:
		tmp = t + (x * (y / z))
	elif z <= -1e+16:
		tmp = x + ((t - x) * (y / a))
	elif (z <= -2.2e-73) or not (z <= 1.65e-18):
		tmp = t - ((y * (t - x)) / z)
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (z <= -1e+16)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif ((z <= -2.2e-73) || !(z <= 1.65e-18))
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t + (x * (y / z));
	elseif (z <= -1e+16)
		tmp = x + ((t - x) * (y / a));
	elseif ((z <= -2.2e-73) || ~((z <= 1.65e-18)))
		tmp = t - ((y * (t - x)) / z);
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+83], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+16], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.2e-73], N[Not[LessEqual[z, 1.65e-18]], $MachinePrecision]], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.79999999999999995e83

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. distribute-lft-out-- 63.6%

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

      3. div-sub 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

      6. distribute-rgt-out-- 63.7%

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

      7. associate-/l* 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in y around inf 76.9%

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

   7. Taylor expanded in t around 0 64.1%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

      3. distribute-rgt-neg-in 72.4%

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

      4. distribute-neg-frac 72.4%

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

   9. Simplified 72.4%

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

   if -8.79999999999999995e83 < z < -1e16

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 53.5%

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

      1. associate-/l* 61.0%

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

      2. associate-/r/ 61.0%

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

   5. Simplified 61.0%

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

   if -1e16 < z < -2.2e-73 or 1.6500000000000001e-18 < z

   1. Initial program 63.2%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. distribute-lft-out-- 69.7%

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

      3. div-sub 69.7%

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

      4. mul-1-neg 69.7%

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

      5. unsub-neg 69.7%

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

      6. distribute-rgt-out-- 69.8%

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

      7. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf 67.4%

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

   7. Taylor expanded in z around 0 61.1%

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

   if -2.2e-73 < z < 1.6500000000000001e-18

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.5%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+16}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-73} \lor \neg \left(z \leq 1.65 \cdot 10^{-18}\right):\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-73} \lor \neg \left(z \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- t x) (/ z y)))))
   (if (<= z -8.8e+83)
     t_1
     (if (<= z -4.9e+20)
       (+ x (* (- t x) (/ y a)))
       (if (or (<= z -1.32e-73) (not (<= z 7e-16)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / y));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -4.9e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -1.32e-73) || !(z <= 7e-16)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - ((t - x) / (z / y))
    if (z <= (-8.8d+83)) then
        tmp = t_1
    else if (z <= (-4.9d+20)) then
        tmp = x + ((t - x) * (y / a))
    else if ((z <= (-1.32d-73)) .or. (.not. (z <= 7d-16))) then
        tmp = t_1
    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 t_1 = t - ((t - x) / (z / y));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -4.9e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= -1.32e-73) || !(z <= 7e-16)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) / (z / y))
	tmp = 0
	if z <= -8.8e+83:
		tmp = t_1
	elif z <= -4.9e+20:
		tmp = x + ((t - x) * (y / a))
	elif (z <= -1.32e-73) or not (z <= 7e-16):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) / Float64(z / y)))
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -4.9e+20)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif ((z <= -1.32e-73) || !(z <= 7e-16))
		tmp = t_1;
	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)
	t_1 = t - ((t - x) / (z / y));
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -4.9e+20)
		tmp = x + ((t - x) * (y / a));
	elseif ((z <= -1.32e-73) || ~((z <= 7e-16)))
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+83], t$95$1, If[LessEqual[z, -4.9e+20], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.32e-73], N[Not[LessEqual[z, 7e-16]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999995e83 or -4.9e20 < z < -1.31999999999999998e-73 or 7.00000000000000035e-16 < z

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. distribute-lft-out-- 66.4%

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

      3. div-sub 66.4%

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

      4. mul-1-neg 66.4%

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

      5. unsub-neg 66.4%

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

      6. distribute-rgt-out-- 66.5%

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

      7. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around inf 70.8%

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

   if -8.79999999999999995e83 < z < -4.9e20

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 71.7%

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

      2. associate-/r/ 71.7%

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

   5. Simplified 71.7%

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

   if -1.31999999999999998e-73 < z < 7.00000000000000035e-16

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.5%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-73} \lor \neg \left(z \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76} \lor \neg \left(z \leq 4.2 \cdot 10^{-18}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -4.8e+69)
     t_1
     (if (<= z -8e-17)
       (/ t (/ (- a z) (- y z)))
       (if (or (<= z -7.8e-76) (not (<= z 4.2e-18)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.8e+69) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = t / ((a - z) / (y - z));
	} else if ((z <= -7.8e-76) || !(z <= 4.2e-18)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    if (z <= (-4.8d+69)) then
        tmp = t_1
    else if (z <= (-8d-17)) then
        tmp = t / ((a - z) / (y - z))
    else if ((z <= (-7.8d-76)) .or. (.not. (z <= 4.2d-18))) then
        tmp = t_1
    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 t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.8e+69) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = t / ((a - z) / (y - z));
	} else if ((z <= -7.8e-76) || !(z <= 4.2e-18)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -4.8e+69:
		tmp = t_1
	elif z <= -8e-17:
		tmp = t / ((a - z) / (y - z))
	elif (z <= -7.8e-76) or not (z <= 4.2e-18):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -4.8e+69)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif ((z <= -7.8e-76) || !(z <= 4.2e-18))
		tmp = t_1;
	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)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -4.8e+69)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = t / ((a - z) / (y - z));
	elseif ((z <= -7.8e-76) || ~((z <= 4.2e-18)))
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+69], t$95$1, If[LessEqual[z, -8e-17], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.8e-76], N[Not[LessEqual[z, 4.2e-18]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e69 or -8.00000000000000057e-17 < z < -7.8000000000000005e-76 or 4.19999999999999999e-18 < z

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. distribute-lft-out-- 66.6%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. distribute-rgt-out-- 66.8%

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

      7. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-*r/ 72.8%

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

      3. *-commutative 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

   8. Simplified 72.8%

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

   if -4.8000000000000003e69 < z < -8.00000000000000057e-17

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 66.9%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

   if -7.8000000000000005e-76 < z < 4.19999999999999999e-18

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.5%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76} \lor \neg \left(z \leq 4.2 \cdot 10^{-18}\right):\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (+ t (* x (/ y z)))))
   (if (<= z -8.8e+83)
     t_2
     (if (<= z -7.4e+17)
       t_1
       (if (<= z -2.5e-74)
         (* (- t x) (/ y (- a z)))
         (if (<= z 1.2e-15) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t + (x * (y / z));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_2;
	} else if (z <= -7.4e+17) {
		tmp = t_1;
	} else if (z <= -2.5e-74) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.2e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t + (x * (y / z))
    if (z <= (-8.8d+83)) then
        tmp = t_2
    else if (z <= (-7.4d+17)) then
        tmp = t_1
    else if (z <= (-2.5d-74)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.2d-15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t + (x * (y / z));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_2;
	} else if (z <= -7.4e+17) {
		tmp = t_1;
	} else if (z <= -2.5e-74) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.2e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t + (x * (y / z))
	tmp = 0
	if z <= -8.8e+83:
		tmp = t_2
	elif z <= -7.4e+17:
		tmp = t_1
	elif z <= -2.5e-74:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.2e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = t_2;
	elseif (z <= -7.4e+17)
		tmp = t_1;
	elseif (z <= -2.5e-74)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.2e-15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t_2;
	elseif (z <= -7.4e+17)
		tmp = t_1;
	elseif (z <= -2.5e-74)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.2e-15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+83], t$95$2, If[LessEqual[z, -7.4e+17], t$95$1, If[LessEqual[z, -2.5e-74], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999995e83 or 1.19999999999999997e-15 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. distribute-lft-out-- 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. distribute-rgt-out-- 66.0%

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

      7. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf 72.6%

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

   7. Taylor expanded in t around 0 59.2%

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

      1. associate-*r/ 65.2%

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

      2. neg-mul-1 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. distribute-neg-frac 65.2%

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

   9. Simplified 65.2%

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

   if -8.79999999999999995e83 < z < -7.4e17 or -2.49999999999999999e-74 < z < 1.19999999999999997e-15

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. associate-/l* 76.6%

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

      2. associate-/r/ 76.3%

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

   5. Simplified 76.3%

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

   if -7.4e17 < z < -2.49999999999999999e-74

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. div-sub 51.5%

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

      2. associate-*r/ 47.3%

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

      3. associate-/l* 51.7%

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

      4. associate-/r/ 51.7%

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

   5. Simplified 51.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))))
   (if (<= z -9.6e+83)
     t_1
     (if (<= z -4.4e+17)
       (+ x (* (- t x) (/ y a)))
       (if (<= z -3.1e-73)
         (* (- t x) (/ y (- a z)))
         (if (<= z 1.22e-15) (+ x (/ y (/ a (- t x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -9.6e+83) {
		tmp = t_1;
	} else if (z <= -4.4e+17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -3.1e-73) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.22e-15) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    if (z <= (-9.6d+83)) then
        tmp = t_1
    else if (z <= (-4.4d+17)) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= (-3.1d-73)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.22d-15) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -9.6e+83) {
		tmp = t_1;
	} else if (z <= -4.4e+17) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= -3.1e-73) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.22e-15) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	tmp = 0
	if z <= -9.6e+83:
		tmp = t_1
	elif z <= -4.4e+17:
		tmp = x + ((t - x) * (y / a))
	elif z <= -3.1e-73:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.22e-15:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -9.6e+83)
		tmp = t_1;
	elseif (z <= -4.4e+17)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= -3.1e-73)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.22e-15)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -9.6e+83)
		tmp = t_1;
	elseif (z <= -4.4e+17)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= -3.1e-73)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.22e-15)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+83], t$95$1, If[LessEqual[z, -4.4e+17], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-73], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-15], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.59999999999999965e83 or 1.21999999999999991e-15 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. distribute-lft-out-- 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. distribute-rgt-out-- 66.0%

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

      7. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf 72.6%

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

   7. Taylor expanded in t around 0 59.2%

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

      1. associate-*r/ 65.2%

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

      2. neg-mul-1 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. distribute-neg-frac 65.2%

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

   9. Simplified 65.2%

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

   if -9.59999999999999965e83 < z < -4.4e17

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 58.1%

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

      1. associate-/l* 66.3%

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

      2. associate-/r/ 66.3%

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

   5. Simplified 66.3%

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

   if -4.4e17 < z < -3.09999999999999969e-73

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. div-sub 51.5%

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

      2. associate-*r/ 47.3%

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

      3. associate-/l* 51.7%

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

      4. associate-/r/ 51.7%

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

   5. Simplified 51.7%

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

   if -3.09999999999999969e-73 < z < 1.21999999999999991e-15

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 74.5%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -2.5e+106)
     t
     (if (<= z -2e-193)
       x
       (if (<= z 9.2e-179)
         t_1
         (if (<= z 7.5e-37) x (if (<= z 4.2e-10) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= -2e-193) {
		tmp = x;
	} else if (z <= 9.2e-179) {
		tmp = t_1;
	} else if (z <= 7.5e-37) {
		tmp = x;
	} else if (z <= 4.2e-10) {
		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 * (t / a)
    if (z <= (-2.5d+106)) then
        tmp = t
    else if (z <= (-2d-193)) then
        tmp = x
    else if (z <= 9.2d-179) then
        tmp = t_1
    else if (z <= 7.5d-37) then
        tmp = x
    else if (z <= 4.2d-10) 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 * (t / a);
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= -2e-193) {
		tmp = x;
	} else if (z <= 9.2e-179) {
		tmp = t_1;
	} else if (z <= 7.5e-37) {
		tmp = x;
	} else if (z <= 4.2e-10) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -2.5e+106:
		tmp = t
	elif z <= -2e-193:
		tmp = x
	elif z <= 9.2e-179:
		tmp = t_1
	elif z <= 7.5e-37:
		tmp = x
	elif z <= 4.2e-10:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= -2e-193)
		tmp = x;
	elseif (z <= 9.2e-179)
		tmp = t_1;
	elseif (z <= 7.5e-37)
		tmp = x;
	elseif (z <= 4.2e-10)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= -2e-193)
		tmp = x;
	elseif (z <= 9.2e-179)
		tmp = t_1;
	elseif (z <= 7.5e-37)
		tmp = x;
	elseif (z <= 4.2e-10)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+106], t, If[LessEqual[z, -2e-193], x, If[LessEqual[z, 9.2e-179], t$95$1, If[LessEqual[z, 7.5e-37], x, If[LessEqual[z, 4.2e-10], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e106 or 4.2e-10 < z

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -2.4999999999999999e106 < z < -2.0000000000000001e-193 or 9.1999999999999995e-179 < z < 7.5000000000000004e-37

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 34.6%

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

   if -2.0000000000000001e-193 < z < 9.1999999999999995e-179 or 7.5000000000000004e-37 < z < 4.2e-10

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 56.4%

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

   4. Taylor expanded in a around inf 54.5%

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

      1. associate-/l* 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in y around inf 52.5%

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

      1. associate-*l/ 54.3%

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

      2. *-commutative 54.3%

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

   9. Simplified 54.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= z -1.1e+106)
     t
     (if (<= z -3.2e-193)
       x
       (if (<= z 3e-176)
         t_1
         (if (<= z 1.82e-37) x (if (<= z 1.5e-12) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (z <= -1.1e+106) {
		tmp = t;
	} else if (z <= -3.2e-193) {
		tmp = x;
	} else if (z <= 3e-176) {
		tmp = t_1;
	} else if (z <= 1.82e-37) {
		tmp = x;
	} else if (z <= 1.5e-12) {
		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 = t / (a / y)
    if (z <= (-1.1d+106)) then
        tmp = t
    else if (z <= (-3.2d-193)) then
        tmp = x
    else if (z <= 3d-176) then
        tmp = t_1
    else if (z <= 1.82d-37) then
        tmp = x
    else if (z <= 1.5d-12) 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 = t / (a / y);
	double tmp;
	if (z <= -1.1e+106) {
		tmp = t;
	} else if (z <= -3.2e-193) {
		tmp = x;
	} else if (z <= 3e-176) {
		tmp = t_1;
	} else if (z <= 1.82e-37) {
		tmp = x;
	} else if (z <= 1.5e-12) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if z <= -1.1e+106:
		tmp = t
	elif z <= -3.2e-193:
		tmp = x
	elif z <= 3e-176:
		tmp = t_1
	elif z <= 1.82e-37:
		tmp = x
	elif z <= 1.5e-12:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (z <= -1.1e+106)
		tmp = t;
	elseif (z <= -3.2e-193)
		tmp = x;
	elseif (z <= 3e-176)
		tmp = t_1;
	elseif (z <= 1.82e-37)
		tmp = x;
	elseif (z <= 1.5e-12)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (z <= -1.1e+106)
		tmp = t;
	elseif (z <= -3.2e-193)
		tmp = x;
	elseif (z <= 3e-176)
		tmp = t_1;
	elseif (z <= 1.82e-37)
		tmp = x;
	elseif (z <= 1.5e-12)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+106], t, If[LessEqual[z, -3.2e-193], x, If[LessEqual[z, 3e-176], t$95$1, If[LessEqual[z, 1.82e-37], x, If[LessEqual[z, 1.5e-12], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999996e106 or 1.5000000000000001e-12 < z

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -1.09999999999999996e106 < z < -3.20000000000000006e-193 or 3e-176 < z < 1.82000000000000002e-37

   1. Initial program 84.6%

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

   3. Taylor expanded in a around inf 34.9%

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

   if -3.20000000000000006e-193 < z < 3e-176 or 1.82000000000000002e-37 < z < 1.5000000000000001e-12

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 55.4%

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

   4. Taylor expanded in a around inf 53.6%

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

      1. associate-/l* 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in y around inf 56.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -12 \lor \neg \left(z \leq 2.4 \cdot 10^{-10}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* y (/ t z)))))
   (if (<= z -4.3e+107)
     t_1
     (if (<= z -2e+20)
       (- x (/ x (/ a y)))
       (if (or (<= z -12.0) (not (<= z 2.4e-10))) t_1 (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y * (t / z));
	double tmp;
	if (z <= -4.3e+107) {
		tmp = t_1;
	} else if (z <= -2e+20) {
		tmp = x - (x / (a / y));
	} else if ((z <= -12.0) || !(z <= 2.4e-10)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (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 = t - (y * (t / z))
    if (z <= (-4.3d+107)) then
        tmp = t_1
    else if (z <= (-2d+20)) then
        tmp = x - (x / (a / y))
    else if ((z <= (-12.0d0)) .or. (.not. (z <= 2.4d-10))) then
        tmp = t_1
    else
        tmp = x + (t * (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 = t - (y * (t / z));
	double tmp;
	if (z <= -4.3e+107) {
		tmp = t_1;
	} else if (z <= -2e+20) {
		tmp = x - (x / (a / y));
	} else if ((z <= -12.0) || !(z <= 2.4e-10)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y * (t / z))
	tmp = 0
	if z <= -4.3e+107:
		tmp = t_1
	elif z <= -2e+20:
		tmp = x - (x / (a / y))
	elif (z <= -12.0) or not (z <= 2.4e-10):
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -4.3e+107)
		tmp = t_1;
	elseif (z <= -2e+20)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif ((z <= -12.0) || !(z <= 2.4e-10))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y * (t / z));
	tmp = 0.0;
	if (z <= -4.3e+107)
		tmp = t_1;
	elseif (z <= -2e+20)
		tmp = x - (x / (a / y));
	elseif ((z <= -12.0) || ~((z <= 2.4e-10)))
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+107], t$95$1, If[LessEqual[z, -2e+20], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -12.0], N[Not[LessEqual[z, 2.4e-10]], $MachinePrecision]], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e107 or -2e20 < z < -12 or 2.4e-10 < z

   1. Initial program 66.1%

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

   3. Taylor expanded in z around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. distribute-lft-out-- 66.3%

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

      3. div-sub 66.3%

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

      4. mul-1-neg 66.3%

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

      5. unsub-neg 66.3%

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

      6. distribute-rgt-out-- 66.4%

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

      7. associate-/l* 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in y around inf 72.9%

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

   7. Taylor expanded in t around inf 52.4%

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

      1. associate-*l/ 59.2%

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

      2. *-commutative 59.2%

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

   9. Simplified 59.2%

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

   if -4.3e107 < z < -2e20

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 52.8%

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

      1. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. unsub-neg 45.8%

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

      3. associate-/l* 52.4%

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

   8. Simplified 52.4%

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

   if -12 < z < 2.4e-10

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around inf 60.7%

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

      1. associate-*r/ 65.4%

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

   8. Simplified 65.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+107}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -12 \lor \neg \left(z \leq 2.4 \cdot 10^{-10}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.6 \lor \neg \left(z \leq 5.8 \cdot 10^{-7}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+106)
   (/ (- t) (+ (/ a z) -1.0))
   (if (<= z -1.2e+19)
     (- x (/ x (/ a y)))
     (if (or (<= z -7.6) (not (<= z 5.8e-7)))
       (- t (* y (/ t z)))
       (+ x (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+106) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -1.2e+19) {
		tmp = x - (x / (a / y));
	} else if ((z <= -7.6) || !(z <= 5.8e-7)) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+106)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if (z <= (-1.2d+19)) then
        tmp = x - (x / (a / y))
    else if ((z <= (-7.6d0)) .or. (.not. (z <= 5.8d-7))) then
        tmp = t - (y * (t / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+106) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -1.2e+19) {
		tmp = x - (x / (a / y));
	} else if ((z <= -7.6) || !(z <= 5.8e-7)) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+106:
		tmp = -t / ((a / z) + -1.0)
	elif z <= -1.2e+19:
		tmp = x - (x / (a / y))
	elif (z <= -7.6) or not (z <= 5.8e-7):
		tmp = t - (y * (t / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+106)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif (z <= -1.2e+19)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif ((z <= -7.6) || !(z <= 5.8e-7))
		tmp = Float64(t - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+106)
		tmp = -t / ((a / z) + -1.0);
	elseif (z <= -1.2e+19)
		tmp = x - (x / (a / y));
	elseif ((z <= -7.6) || ~((z <= 5.8e-7)))
		tmp = t - (y * (t / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+106], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e+19], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.6], N[Not[LessEqual[z, 5.8e-7]], $MachinePrecision]], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4999999999999999e106

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0 32.8%

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

   4. Taylor expanded in y around 0 31.0%

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

      1. mul-1-neg 31.0%

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

      2. associate-/l* 64.8%

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

      3. div-sub 64.8%

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

      4. sub-neg 64.8%

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

      5. *-inverses 64.8%

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

      6. metadata-eval 64.8%

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

   6. Simplified 64.8%

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

   if -2.4999999999999999e106 < z < -1.2e19

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 52.8%

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

      1. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. unsub-neg 45.8%

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

      3. associate-/l* 52.4%

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

   8. Simplified 52.4%

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

   if -1.2e19 < z < -7.5999999999999996 or 5.7999999999999995e-7 < z

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. distribute-lft-out-- 67.6%

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

      3. div-sub 67.6%

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

      4. mul-1-neg 67.6%

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

      5. unsub-neg 67.6%

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

      6. distribute-rgt-out-- 67.7%

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

      7. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in y around inf 70.0%

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

   7. Taylor expanded in t around inf 50.7%

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

      1. associate-*l/ 55.7%

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

      2. *-commutative 55.7%

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

   9. Simplified 55.7%

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

   if -7.5999999999999996 < z < 5.7999999999999995e-7

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around inf 60.7%

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

      1. associate-*r/ 65.4%

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

   8. Simplified 65.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.6 \lor \neg \left(z \leq 5.8 \cdot 10^{-7}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ y z)))))
   (if (<= z -8.8e+83)
     t_1
     (if (<= z -3.5e+16)
       (- x (/ x (/ a y)))
       (if (<= z -4.8e-74)
         (* (- t x) (/ y (- a z)))
         (if (<= z 2.8e-9) (+ x (* t (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = x - (x / (a / y));
	} else if (z <= -4.8e-74) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.8e-9) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * (y / z))
    if (z <= (-8.8d+83)) then
        tmp = t_1
    else if (z <= (-3.5d+16)) then
        tmp = x - (x / (a / y))
    else if (z <= (-4.8d-74)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 2.8d-9) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * (y / z));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = x - (x / (a / y));
	} else if (z <= -4.8e-74) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 2.8e-9) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * (y / z))
	tmp = 0
	if z <= -8.8e+83:
		tmp = t_1
	elif z <= -3.5e+16:
		tmp = x - (x / (a / y))
	elif z <= -4.8e-74:
		tmp = (t - x) * (y / (a - z))
	elif z <= 2.8e-9:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(y / z)))
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= -4.8e-74)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 2.8e-9)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * (y / z));
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = x - (x / (a / y));
	elseif (z <= -4.8e-74)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 2.8e-9)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+83], t$95$1, If[LessEqual[z, -3.5e+16], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-74], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-9], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.79999999999999995e83 or 2.79999999999999984e-9 < z

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. associate--l+ 66.1%

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

      2. distribute-lft-out-- 66.1%

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

      3. div-sub 66.1%

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

      4. mul-1-neg 66.1%

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

      5. unsub-neg 66.1%

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

      6. distribute-rgt-out-- 66.2%

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

      7. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 73.0%

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

   7. Taylor expanded in t around 0 59.3%

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

      1. associate-*r/ 65.4%

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

      2. neg-mul-1 65.4%

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

      3. distribute-rgt-neg-in 65.4%

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

      4. distribute-neg-frac 65.4%

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

   9. Simplified 65.4%

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

   if -8.79999999999999995e83 < z < -3.5e16

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 53.5%

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

      1. associate-/l* 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in t around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. unsub-neg 45.3%

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

      3. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

   if -3.5e16 < z < -4.7999999999999998e-74

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. div-sub 53.8%

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

      2. associate-*r/ 49.4%

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

      3. associate-/l* 54.0%

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

      4. associate-/r/ 54.1%

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

   5. Simplified 54.1%

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

   if -4.7999999999999998e-74 < z < 2.79999999999999984e-9

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around inf 66.3%

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

      1. associate-*r/ 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+208}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+208)
   (- x (* (- t x) (/ z a)))
   (if (<= a -2.4e-53)
     (/ t (/ (- a z) (- y z)))
     (if (<= a 1.65e+24)
       (- t (/ (- t x) (/ z y)))
       (+ x (* (- t x) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+208) {
		tmp = x - ((t - x) * (z / a));
	} else if (a <= -2.4e-53) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.65e+24) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+208)) then
        tmp = x - ((t - x) * (z / a))
    else if (a <= (-2.4d-53)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 1.65d+24) then
        tmp = t - ((t - x) / (z / y))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+208) {
		tmp = x - ((t - x) * (z / a));
	} else if (a <= -2.4e-53) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.65e+24) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+208:
		tmp = x - ((t - x) * (z / a))
	elif a <= -2.4e-53:
		tmp = t / ((a - z) / (y - z))
	elif a <= 1.65e+24:
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+208)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(z / a)));
	elseif (a <= -2.4e-53)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 1.65e+24)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+208)
		tmp = x - ((t - x) * (z / a));
	elseif (a <= -2.4e-53)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 1.65e+24)
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+208], N[(x - N[(N[(t - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-53], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+24], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.00000000000000029e208

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 88.7%

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

      4. associate-/r/ 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in z around 0 77.4%

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

   if -9.00000000000000029e208 < a < -2.40000000000000007e-53

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 49.6%

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

      1. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   if -2.40000000000000007e-53 < a < 1.6499999999999999e24

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. distribute-rgt-out-- 78.6%

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

      7. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around inf 76.2%

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

   if 1.6499999999999999e24 < a

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 55.3%

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

      1. associate-/l* 66.2%

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

      2. associate-/r/ 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+208}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -11.5 \lor \neg \left(z \leq 3.7 \cdot 10^{-13}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -11.5) (not (<= z 3.7e-13)))
   (- t (* y (/ t z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -11.5) || !(z <= 3.7e-13)) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-11.5d0)) .or. (.not. (z <= 3.7d-13))) then
        tmp = t - (y * (t / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -11.5) || !(z <= 3.7e-13)) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -11.5) or not (z <= 3.7e-13):
		tmp = t - (y * (t / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -11.5) || !(z <= 3.7e-13))
		tmp = Float64(t - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -11.5) || ~((z <= 3.7e-13)))
		tmp = t - (y * (t / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -11.5], N[Not[LessEqual[z, 3.7e-13]], $MachinePrecision]], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -11.5 or 3.69999999999999989e-13 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. distribute-lft-out-- 63.4%

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

      3. div-sub 63.4%

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

      4. mul-1-neg 63.4%

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

      5. unsub-neg 63.4%

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

      6. distribute-rgt-out-- 63.5%

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

      7. associate-/l* 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in y around inf 69.5%

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

   7. Taylor expanded in t around inf 49.6%

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

      1. associate-*l/ 55.7%

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

      2. *-commutative 55.7%

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

   9. Simplified 55.7%

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

   if -11.5 < z < 3.69999999999999989e-13

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around inf 60.7%

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

      1. associate-*r/ 65.4%

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

   8. Simplified 65.4%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11.5 \lor \neg \left(z \leq 3.7 \cdot 10^{-13}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+106) t (if (<= z 3.6e-6) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= 3.6e-6) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+106)) then
        tmp = t
    else if (z <= 3.6d-6) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+106) {
		tmp = t;
	} else if (z <= 3.6e-6) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+106:
		tmp = t
	elif z <= 3.6e-6:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= 3.6e-6)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+106)
		tmp = t;
	elseif (z <= 3.6e-6)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+106], t, If[LessEqual[z, 3.6e-6], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e106 or 3.59999999999999984e-6 < z

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -2.4999999999999999e106 < z < 3.59999999999999984e-6

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 63.6%

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

      1. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in t around inf 57.4%

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

      1. associate-*r/ 61.3%

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

   8. Simplified 61.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+107) t (if (<= z 6.2e-23) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+107) {
		tmp = t;
	} else if (z <= 6.2e-23) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d+107)) then
        tmp = t
    else if (z <= 6.2d-23) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+107) {
		tmp = t;
	} else if (z <= 6.2e-23) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+107:
		tmp = t
	elif z <= 6.2e-23:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+107)
		tmp = t;
	elseif (z <= 6.2e-23)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+107)
		tmp = t;
	elseif (z <= 6.2e-23)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+107], t, If[LessEqual[z, 6.2e-23], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3e107 or 6.1999999999999998e-23 < z

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -4.3e107 < z < 6.1999999999999998e-23

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf 31.1%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 2.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.7%

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

3. Taylor expanded in y around 0 35.4%

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

   1. mul-1-neg 35.4%

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

   2. unsub-neg 35.4%

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

   3. associate-/l* 47.5%

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

   4. associate-/r/ 46.4%

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

5. Simplified 46.4%

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

6. Taylor expanded in t around 0 20.1%

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

   1. sub-neg 20.1%

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

   2. mul-1-neg 20.1%

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

   3. remove-double-neg 20.1%

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

   4. associate-/l* 22.1%

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

   5. div-sub 22.1%

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

   6. sub-neg 22.1%

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

   7. *-inverses 22.1%

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

   8. metadata-eval 22.1%

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

8. Simplified 22.1%

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

9. Taylor expanded in a around 0 2.8%

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

    1. distribute-rgt1-in 2.8%

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

    2. metadata-eval 2.8%

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

    3. mul0-lft 2.8%

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

11. Simplified 2.8%

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

12. Final simplification 2.8%

    \[\leadsto 0 \]
13. Add Preprocessing

Alternative 23: 24.8% 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 77.7%

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

3. Taylor expanded in z around inf 27.9%

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

4. Final simplification 27.9%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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)))))