Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.7% → 99.7%

Time: 9.2s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+300}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+300)))
     (+ x (/ (- y z) (/ (- a z) t)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+300)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+300)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+300):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+300))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+300)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+300]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.0000000000000002e300 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 49.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.0000000000000002e300

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 4 \cdot 10^{+300}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+266}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+266)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+266)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+266)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+266):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+266))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+266)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+266]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.0000000000000001e266 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 49.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.0000000000000001e266

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 4 \cdot 10^{+266}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00054:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00054)
   (+ t x)
   (if (<= z -1.7e-104)
     (+ x (* y (/ t a)))
     (if (<= z -2e-112)
       (* t (- 1.0 (/ y z)))
       (if (<= z 1.75e-22) (+ x (* t (/ y a))) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00054) {
		tmp = t + x;
	} else if (z <= -1.7e-104) {
		tmp = x + (y * (t / a));
	} else if (z <= -2e-112) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.75e-22) {
		tmp = x + (t * (y / a));
	} else {
		tmp = 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 <= (-0.00054d0)) then
        tmp = t + x
    else if (z <= (-1.7d-104)) then
        tmp = x + (y * (t / a))
    else if (z <= (-2d-112)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.75d-22) then
        tmp = x + (t * (y / a))
    else
        tmp = 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 <= -0.00054) {
		tmp = t + x;
	} else if (z <= -1.7e-104) {
		tmp = x + (y * (t / a));
	} else if (z <= -2e-112) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.75e-22) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00054:
		tmp = t + x
	elif z <= -1.7e-104:
		tmp = x + (y * (t / a))
	elif z <= -2e-112:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.75e-22:
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00054)
		tmp = Float64(t + x);
	elseif (z <= -1.7e-104)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= -2e-112)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.75e-22)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00054)
		tmp = t + x;
	elseif (z <= -1.7e-104)
		tmp = x + (y * (t / a));
	elseif (z <= -2e-112)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.75e-22)
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00054], N[(t + x), $MachinePrecision], If[LessEqual[z, -1.7e-104], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-112], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-22], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.40000000000000007e-4 or 1.75000000000000003e-22 < z

   1. Initial program 77.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -5.40000000000000007e-4 < z < -1.70000000000000008e-104

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

   if -1.70000000000000008e-104 < z < -1.9999999999999999e-112

   1. Initial program 99.6%

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

      1. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in a around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in x around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. associate-/l* 76.1%

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

      3. *-commutative 76.1%

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

      4. div-sub 76.1%

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

      5. sub-neg 76.1%

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

      6. *-inverses 76.1%

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

      7. metadata-eval 76.1%

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

      8. distribute-lft-neg-in 76.1%

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

      9. *-commutative 76.1%

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

      10. +-commutative 76.1%

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

      11. distribute-neg-in 76.1%

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

      12. metadata-eval 76.1%

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

      13. sub-neg 76.1%

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

   10. Simplified 76.1%

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

   if -1.9999999999999999e-112 < z < 1.75000000000000003e-22

   1. Initial program 96.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. clear-num 95.7%

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

      2. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 76.2%

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

   9. Simplified 76.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00054:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.046:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.046)
   (+ t x)
   (if (<= z -1.7e-104)
     (+ x (/ y (/ a t)))
     (if (<= z -2e-112)
       (* t (- 1.0 (/ y z)))
       (if (<= z 1.75e-20) (+ x (* t (/ y a))) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.046) {
		tmp = t + x;
	} else if (z <= -1.7e-104) {
		tmp = x + (y / (a / t));
	} else if (z <= -2e-112) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.75e-20) {
		tmp = x + (t * (y / a));
	} else {
		tmp = 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 <= (-0.046d0)) then
        tmp = t + x
    else if (z <= (-1.7d-104)) then
        tmp = x + (y / (a / t))
    else if (z <= (-2d-112)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.75d-20) then
        tmp = x + (t * (y / a))
    else
        tmp = 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 <= -0.046) {
		tmp = t + x;
	} else if (z <= -1.7e-104) {
		tmp = x + (y / (a / t));
	} else if (z <= -2e-112) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.75e-20) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.046:
		tmp = t + x
	elif z <= -1.7e-104:
		tmp = x + (y / (a / t))
	elif z <= -2e-112:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.75e-20:
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.046)
		tmp = Float64(t + x);
	elseif (z <= -1.7e-104)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -2e-112)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.75e-20)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.046)
		tmp = t + x;
	elseif (z <= -1.7e-104)
		tmp = x + (y / (a / t));
	elseif (z <= -2e-112)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.75e-20)
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.046], N[(t + x), $MachinePrecision], If[LessEqual[z, -1.7e-104], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-112], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-20], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.045999999999999999 or 1.75000000000000002e-20 < z

   1. Initial program 77.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -0.045999999999999999 < z < -1.70000000000000008e-104

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

      1. clear-num 78.4%

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

      2. un-div-inv 78.4%

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

   9. Applied egg-rr 78.4%

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

   if -1.70000000000000008e-104 < z < -1.9999999999999999e-112

   1. Initial program 99.6%

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

      1. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in a around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in x around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. associate-/l* 76.1%

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

      3. *-commutative 76.1%

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

      4. div-sub 76.1%

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

      5. sub-neg 76.1%

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

      6. *-inverses 76.1%

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

      7. metadata-eval 76.1%

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

      8. distribute-lft-neg-in 76.1%

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

      9. *-commutative 76.1%

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

      10. +-commutative 76.1%

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

      11. distribute-neg-in 76.1%

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

      12. metadata-eval 76.1%

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

      13. sub-neg 76.1%

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

   10. Simplified 76.1%

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

   if -1.9999999999999999e-112 < z < 1.75000000000000002e-20

   1. Initial program 96.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. clear-num 95.7%

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

      2. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 76.2%

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

   9. Simplified 76.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.046:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+121}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.37)
   (+ t x)
   (if (<= z 2.9e-91)
     (+ x (* t (/ y a)))
     (if (<= z 7e+121) (- x (* t (/ y z))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.37) {
		tmp = t + x;
	} else if (z <= 2.9e-91) {
		tmp = x + (t * (y / a));
	} else if (z <= 7e+121) {
		tmp = x - (t * (y / z));
	} else {
		tmp = 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 <= (-0.37d0)) then
        tmp = t + x
    else if (z <= 2.9d-91) then
        tmp = x + (t * (y / a))
    else if (z <= 7d+121) then
        tmp = x - (t * (y / z))
    else
        tmp = 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 <= -0.37) {
		tmp = t + x;
	} else if (z <= 2.9e-91) {
		tmp = x + (t * (y / a));
	} else if (z <= 7e+121) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.37:
		tmp = t + x
	elif z <= 2.9e-91:
		tmp = x + (t * (y / a))
	elif z <= 7e+121:
		tmp = x - (t * (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.37)
		tmp = Float64(t + x);
	elseif (z <= 2.9e-91)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 7e+121)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.37)
		tmp = t + x;
	elseif (z <= 2.9e-91)
		tmp = x + (t * (y / a));
	elseif (z <= 7e+121)
		tmp = x - (t * (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.37], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.9e-91], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+121], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.37 or 6.9999999999999999e121 < z

   1. Initial program 73.9%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 83.6%

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

   if -0.37 < z < 2.9000000000000001e-91

   1. Initial program 97.0%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 75.3%

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

   9. Simplified 75.3%

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

   if 2.9000000000000001e-91 < z < 6.9999999999999999e121

   1. Initial program 94.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 84.2%

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

      1. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.37:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+121}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00061:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00061)
   (+ t x)
   (if (<= z 3.6e-91)
     (+ x (* t (/ y a)))
     (if (<= z 1.06e+123) (- x (/ t (/ z y))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00061) {
		tmp = t + x;
	} else if (z <= 3.6e-91) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.06e+123) {
		tmp = x - (t / (z / y));
	} else {
		tmp = 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 <= (-0.00061d0)) then
        tmp = t + x
    else if (z <= 3.6d-91) then
        tmp = x + (t * (y / a))
    else if (z <= 1.06d+123) then
        tmp = x - (t / (z / y))
    else
        tmp = 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 <= -0.00061) {
		tmp = t + x;
	} else if (z <= 3.6e-91) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.06e+123) {
		tmp = x - (t / (z / y));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00061:
		tmp = t + x
	elif z <= 3.6e-91:
		tmp = x + (t * (y / a))
	elif z <= 1.06e+123:
		tmp = x - (t / (z / y))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00061)
		tmp = Float64(t + x);
	elseif (z <= 3.6e-91)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.06e+123)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00061)
		tmp = t + x;
	elseif (z <= 3.6e-91)
		tmp = x + (t * (y / a));
	elseif (z <= 1.06e+123)
		tmp = x - (t / (z / y));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00061], N[(t + x), $MachinePrecision], If[LessEqual[z, 3.6e-91], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+123], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.09999999999999974e-4 or 1.06e123 < z

   1. Initial program 73.9%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 83.6%

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

   if -6.09999999999999974e-4 < z < 3.6e-91

   1. Initial program 97.0%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 75.3%

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

   9. Simplified 75.3%

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

   if 3.6e-91 < z < 1.06e123

   1. Initial program 94.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 84.2%

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

      1. associate-/l* 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 76.1%

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

   10. Simplified 76.1%

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

       1. clear-num 76.1%

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

       2. un-div-inv 76.2%

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

   12. Applied egg-rr 76.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00061:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+172} \lor \neg \left(z \leq 6.4 \cdot 10^{+122}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+172) (not (<= z 6.4e+122)))
   (+ t x)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+172) || !(z <= 6.4e+122)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d+172)) .or. (.not. (z <= 6.4d+122))) then
        tmp = t + x
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+172) || !(z <= 6.4e+122)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+172) or not (z <= 6.4e+122):
		tmp = t + x
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+172) || !(z <= 6.4e+122))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e+172) || ~((z <= 6.4e+122)))
		tmp = t + x;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+172], N[Not[LessEqual[z, 6.4e+122]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e172 or 6.40000000000000024e122 < z

   1. Initial program 69.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 91.3%

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

   if -1.6999999999999999e172 < z < 6.40000000000000024e122

   1. Initial program 94.1%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf 83.6%

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

      1. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+172} \lor \neg \left(z \leq 6.4 \cdot 10^{+122}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+173} \lor \neg \left(z \leq 1.6 \cdot 10^{+123}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+173) (not (<= z 1.6e+123)))
   (+ t x)
   (+ x (/ t (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+173) || !(z <= 1.6e+123)) {
		tmp = t + x;
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+173)) .or. (.not. (z <= 1.6d+123))) then
        tmp = t + x
    else
        tmp = x + (t / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+173) || !(z <= 1.6e+123)) {
		tmp = t + x;
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+173) or not (z <= 1.6e+123):
		tmp = t + x
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+173) || !(z <= 1.6e+123))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+173) || ~((z <= 1.6e+123)))
		tmp = t + x;
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+173], N[Not[LessEqual[z, 1.6e+123]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000001e173 or 1.60000000000000002e123 < z

   1. Initial program 69.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 91.3%

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

   if -8.0000000000000001e173 < z < 1.60000000000000002e123

   1. Initial program 94.1%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf 83.6%

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

      1. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

      1. clear-num 84.1%

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

      2. un-div-inv 84.1%

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

   9. Applied egg-rr 84.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+173} \lor \neg \left(z \leq 1.6 \cdot 10^{+123}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+35}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.05e+91)
   (+ x (/ (* y t) (- a z)))
   (if (<= y 1.65e+35) (- x (* t (/ z (- a z)))) (+ x (/ t (/ (- a z) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.05e+91) {
		tmp = x + ((y * t) / (a - z));
	} else if (y <= 1.65e+35) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.05d+91)) then
        tmp = x + ((y * t) / (a - z))
    else if (y <= 1.65d+35) then
        tmp = x - (t * (z / (a - z)))
    else
        tmp = x + (t / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.05e+91) {
		tmp = x + ((y * t) / (a - z));
	} else if (y <= 1.65e+35) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.05e+91:
		tmp = x + ((y * t) / (a - z))
	elif y <= 1.65e+35:
		tmp = x - (t * (z / (a - z)))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.05e+91)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (y <= 1.65e+35)
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.05e+91)
		tmp = x + ((y * t) / (a - z));
	elseif (y <= 1.65e+35)
		tmp = x - (t * (z / (a - z)));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.05e+91], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+35], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0500000000000001e91

   1. Initial program 91.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 91.6%

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

   if -2.0500000000000001e91 < y < 1.6500000000000001e35

   1. Initial program 85.4%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

      3. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   if 1.6500000000000001e35 < y

   1. Initial program 86.0%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around inf 82.4%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

      1. clear-num 89.3%

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

      2. un-div-inv 89.4%

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

   9. Applied egg-rr 89.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+35}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00044 \lor \neg \left(z \leq 1.2 \cdot 10^{-20}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.00044) (not (<= z 1.2e-20))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00044) || !(z <= 1.2e-20)) {
		tmp = t + x;
	} 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 <= (-0.00044d0)) .or. (.not. (z <= 1.2d-20))) then
        tmp = t + x
    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 <= -0.00044) || !(z <= 1.2e-20)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.00044) or not (z <= 1.2e-20):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.00044) || !(z <= 1.2e-20))
		tmp = Float64(t + x);
	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 <= -0.00044) || ~((z <= 1.2e-20)))
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.00044], N[Not[LessEqual[z, 1.2e-20]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000016e-4 or 1.19999999999999996e-20 < z

   1. Initial program 77.5%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -4.40000000000000016e-4 < z < 1.19999999999999996e-20

   1. Initial program 97.5%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

      1. clear-num 95.8%

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

      2. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 72.5%

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

      1. associate-/l* 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00044 \lor \neg \left(z \leq 1.2 \cdot 10^{-20}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+211}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.55e+139)
   (* y (- (/ t z)))
   (if (<= y 4.2e+211) (+ t x) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+139) {
		tmp = y * -(t / z);
	} else if (y <= 4.2e+211) {
		tmp = t + x;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.55d+139)) then
        tmp = y * -(t / z)
    else if (y <= 4.2d+211) then
        tmp = t + x
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+139) {
		tmp = y * -(t / z);
	} else if (y <= 4.2e+211) {
		tmp = t + x;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e+139:
		tmp = y * -(t / z)
	elif y <= 4.2e+211:
		tmp = t + x
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e+139)
		tmp = Float64(y * Float64(-Float64(t / z)));
	elseif (y <= 4.2e+211)
		tmp = Float64(t + x);
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e+139)
		tmp = y * -(t / z);
	elseif (y <= 4.2e+211)
		tmp = t + x;
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e+139], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 4.2e+211], N[(t + x), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e139

   1. Initial program 92.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in a around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf 56.1%

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

      1. mul-1-neg 56.1%

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

   10. Simplified 56.1%

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

       1. associate-/l* 53.9%

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

       2. clear-num 53.8%

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

       3. div-inv 53.9%

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

       4. associate-/r/ 58.7%

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

   12. Applied egg-rr 58.7%

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

   if -1.55e139 < y < 4.2e211

   1. Initial program 86.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 75.1%

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

   if 4.2e211 < y

   1. Initial program 79.6%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in x around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. associate-/l* 71.5%

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

      3. *-commutative 71.5%

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

      4. div-sub 71.5%

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

      5. sub-neg 71.5%

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

      6. *-inverses 71.5%

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

      7. metadata-eval 71.5%

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

      8. distribute-lft-neg-in 71.5%

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

      9. *-commutative 71.5%

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

      10. +-commutative 71.5%

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

      11. distribute-neg-in 71.5%

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

      12. metadata-eval 71.5%

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

      13. sub-neg 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+211}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+139} \lor \neg \left(y \leq 2.6 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.22e+139) (not (<= y 2.6e+213))) (* y (- (/ t z))) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.22e+139) || !(y <= 2.6e+213)) {
		tmp = y * -(t / z);
	} else {
		tmp = 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 ((y <= (-1.22d+139)) .or. (.not. (y <= 2.6d+213))) then
        tmp = y * -(t / z)
    else
        tmp = 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 ((y <= -1.22e+139) || !(y <= 2.6e+213)) {
		tmp = y * -(t / z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.22e+139) or not (y <= 2.6e+213):
		tmp = y * -(t / z)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.22e+139) || !(y <= 2.6e+213))
		tmp = Float64(y * Float64(-Float64(t / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.22e+139) || ~((y <= 2.6e+213)))
		tmp = y * -(t / z);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.22e+139], N[Not[LessEqual[y, 2.6e+213]], $MachinePrecision]], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2200000000000001e139 or 2.59999999999999999e213 < y

   1. Initial program 88.4%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. unsub-neg 70.4%

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

      3. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 56.5%

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

      1. mul-1-neg 56.5%

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

   10. Simplified 56.5%

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

       1. associate-/l* 58.7%

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

       2. clear-num 58.6%

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

       3. div-inv 58.8%

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

       4. associate-/r/ 58.5%

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

   12. Applied egg-rr 58.5%

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

   if -1.2200000000000001e139 < y < 2.59999999999999999e213

   1. Initial program 86.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 75.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+139} \lor \neg \left(y \leq 2.6 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.1e+137)
   (* y (- (/ t z)))
   (if (<= y 1.3e+211) (+ t x) (* t (/ y (- z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.1e+137) {
		tmp = y * -(t / z);
	} else if (y <= 1.3e+211) {
		tmp = t + x;
	} else {
		tmp = t * (y / -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.1d+137)) then
        tmp = y * -(t / z)
    else if (y <= 1.3d+211) then
        tmp = t + x
    else
        tmp = t * (y / -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.1e+137) {
		tmp = y * -(t / z);
	} else if (y <= 1.3e+211) {
		tmp = t + x;
	} else {
		tmp = t * (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.1e+137:
		tmp = y * -(t / z)
	elif y <= 1.3e+211:
		tmp = t + x
	else:
		tmp = t * (y / -z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.1e+137)
		tmp = Float64(y * Float64(-Float64(t / z)));
	elseif (y <= 1.3e+211)
		tmp = Float64(t + x);
	else
		tmp = Float64(t * Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.1e+137)
		tmp = y * -(t / z);
	elseif (y <= 1.3e+211)
		tmp = t + x;
	else
		tmp = t * (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.1e+137], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 1.3e+211], N[(t + x), $MachinePrecision], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.10000000000000007e137

   1. Initial program 92.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in a around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf 56.1%

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

      1. mul-1-neg 56.1%

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

   10. Simplified 56.1%

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

       1. associate-/l* 53.9%

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

       2. clear-num 53.8%

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

       3. div-inv 53.9%

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

       4. associate-/r/ 58.7%

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

   12. Applied egg-rr 58.7%

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

   if -7.10000000000000007e137 < y < 1.2999999999999999e211

   1. Initial program 86.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 75.1%

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

   if 1.2999999999999999e211 < y

   1. Initial program 79.6%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. associate-*r/ 70.8%

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

      3. distribute-rgt-neg-in 70.8%

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

   10. Simplified 70.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

   1. associate-/l* 95.6%

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

3. Simplified 95.6%

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

5. Final simplification 95.6%

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

Alternative 15: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.96 \cdot 10^{+173}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.96e+173) x (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.96e+173) {
		tmp = x;
	} else {
		tmp = 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 (a <= (-1.96d+173)) then
        tmp = x
    else
        tmp = 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 (a <= -1.96e+173) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.96e+173:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.96e+173)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.96e+173)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.96e+173], x, N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.96e173

   1. Initial program 80.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 75.5%

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

   if -1.96e173 < a

   1. Initial program 87.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 65.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.96 \cdot 10^{+173}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

   1. associate-/l* 95.6%

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

3. Simplified 95.6%

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

5. Taylor expanded in x around inf 48.3%

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

6. Final simplification 48.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))