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

Percentage Accurate: 85.4% → 99.6%

Time: 7.0s

Alternatives: 11

Speedup: 0.7×

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: 85.4% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{t}{a - z}}{\frac{1}{y - z}} + x\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (/ t (- a z)) (/ 1.0 (- y z))) x))
        (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 4e+291) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t / (a - z)) / (1.0 / (y - z))) + x;
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t / (a - z)) / (1.0 / (y - z))) + x;
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t / (a - z)) / (1.0 / (y - z))) + x
	t_2 = (t * (y - z)) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 4e+291:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t / Float64(a - z)) / Float64(1.0 / Float64(y - z))) + x)
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((t / (a - z)) / (1.0 / (y - z))) + x;
	t_2 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 4e+291], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 3.9999999999999998e291 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 33.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. clear-num N/A

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

      12. flip-- N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.9999999999999998e291

   1. Initial program 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\frac{\frac{t}{a - z}}{\frac{1}{y - z}} + x\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t}{a - z}}{\frac{1}{y - z}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+249}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))) (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 4e+249) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 4e+249) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 4e+249) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	t_2 = (t * (y - z)) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 4e+249:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 4e+249)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	t_2 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 4e+249)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 4e+249], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 3.9999999999999997e249 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 36.0%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   7. Applied rewrites 80.0%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.9999999999999997e249

   1. Initial program 98.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 4 \cdot 10^{+249}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))) (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 -4e+288) t_1 (if (<= t_2 4e+291) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -4e+288) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t / (a - z)) * (y - z)
    t_2 = (t * (y - z)) / (a - z)
    if (t_2 <= (-4d+288)) then
        tmp = t_1
    else if (t_2 <= 4d+291) then
        tmp = x + t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -4e+288) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / (a - z)) * (y - z)
	t_2 = (t * (y - z)) / (a - z)
	tmp = 0
	if t_2 <= -4e+288:
		tmp = t_1
	elif t_2 <= 4e+291:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -4e+288)
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / (a - z)) * (y - z);
	t_2 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if (t_2 <= -4e+288)
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+288], t$95$1, If[LessEqual[t$95$2, 4e+291], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4e288 or 3.9999999999999998e291 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 34.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -4e288 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.9999999999999998e291

   1. Initial program 98.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -4 \cdot 10^{+288}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+74)
   (+ x t)
   (if (<= z 2.8e-73)
     (fma (/ y a) t x)
     (if (<= z 2.05e+200) (fma (/ y (- z)) t x) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+74) {
		tmp = x + t;
	} else if (z <= 2.8e-73) {
		tmp = fma((y / a), t, x);
	} else if (z <= 2.05e+200) {
		tmp = fma((y / -z), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+74)
		tmp = Float64(x + t);
	elseif (z <= 2.8e-73)
		tmp = fma(Float64(y / a), t, x);
	elseif (z <= 2.05e+200)
		tmp = fma(Float64(y / Float64(-z)), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+74], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.8e-73], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 2.05e+200], N[(N[(y / (-z)), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e74 or 2.0500000000000001e200 < z

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if -8.9999999999999999e74 < z < 2.80000000000000012e-73

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if 2.80000000000000012e-73 < z < 2.0500000000000001e200

   1. Initial program 83.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{y - z}{z}}, t, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)}, t, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)} + 1, t, x\right) \]

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)}, t, x\right) \]

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a - z} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ y z)) t x)))
   (if (<= z -4.1e+75)
     t_1
     (if (<= z 1.26e+178) (+ (* (/ y (- a z)) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((1.0 - (y / z)), t, x);
	double tmp;
	if (z <= -4.1e+75) {
		tmp = t_1;
	} else if (z <= 1.26e+178) {
		tmp = ((y / (a - z)) * t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(1.0 - Float64(y / z)), t, x)
	tmp = 0.0
	if (z <= -4.1e+75)
		tmp = t_1;
	elseif (z <= 1.26e+178)
		tmp = Float64(Float64(Float64(y / Float64(a - z)) * t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -4.1e+75], t$95$1, If[LessEqual[z, 1.26e+178], N[(N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999998e75 or 1.26e178 < z

   1. Initial program 58.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{y - z}{z}}, t, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)}, t, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)} + 1, t, x\right) \]

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)}, t, x\right) \]

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 93.0

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

   5. Applied rewrites 93.0%

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

   if -4.0999999999999998e75 < z < 1.26e178

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 90.2

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

   5. Applied rewrites 90.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+178}:\\ \;\;\;\;\frac{y}{a - z} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \mathbf{if}\;a \leq -1.14 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) a) t x)))
   (if (<= a -1.14e-35) t_1 (if (<= a 1e-16) (fma (- 1.0 (/ y z)) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / a), t, x);
	double tmp;
	if (a <= -1.14e-35) {
		tmp = t_1;
	} else if (a <= 1e-16) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / a), t, x)
	tmp = 0.0
	if (a <= -1.14e-35)
		tmp = t_1;
	elseif (a <= 1e-16)
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[a, -1.14e-35], t$95$1, If[LessEqual[a, 1e-16], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14e-35 or 9.9999999999999998e-17 < a

   1. Initial program 81.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -1.14e-35 < a < 9.9999999999999998e-17

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{y - z}{z}}, t, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)}, t, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)} + 1, t, x\right) \]

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)}, t, x\right) \]

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 86.3

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

   5. Applied rewrites 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-35)
   (fma (/ t a) y x)
   (if (<= a 3.4e-16) (fma (- 1.0 (/ y z)) t x) (fma (/ y a) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-35) {
		tmp = fma((t / a), y, x);
	} else if (a <= 3.4e-16) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-35)
		tmp = fma(Float64(t / a), y, x);
	elseif (a <= 3.4e-16)
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-35], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[a, 3.4e-16], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.09999999999999997e-35

   1. Initial program 79.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. clear-num N/A

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

      12. flip-- N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 96.3

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

   4. Applied rewrites 96.3%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 81.8

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

   7. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 81.8%

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

   if -1.09999999999999997e-35 < a < 3.4e-16

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{y - z}{z}}, t, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)}, t, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)} + 1, t, x\right) \]

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{y}{z}\right)\right)}, t, x\right) \]

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if 3.4e-16 < a

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 83.1

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

   5. Applied rewrites 83.1%

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

Alternative 8: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+74) (+ x t) (if (<= z 0.47) (fma (/ y a) t x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+74) {
		tmp = x + t;
	} else if (z <= 0.47) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+74)
		tmp = Float64(x + t);
	elseif (z <= 0.47)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+74], N[(x + t), $MachinePrecision], If[LessEqual[z, 0.47], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999999e74 or 0.46999999999999997 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -8.9999999999999999e74 < z < 0.46999999999999997

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-285}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-86) (+ x t) (if (<= z -1.62e-285) (* (/ y a) t) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-86) {
		tmp = x + t;
	} else if (z <= -1.62e-285) {
		tmp = (y / a) * t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d-86)) then
        tmp = x + t
    else if (z <= (-1.62d-285)) then
        tmp = (y / a) * t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-86) {
		tmp = x + t;
	} else if (z <= -1.62e-285) {
		tmp = (y / a) * t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-86:
		tmp = x + t
	elif z <= -1.62e-285:
		tmp = (y / a) * t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-86)
		tmp = Float64(x + t);
	elseif (z <= -1.62e-285)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e-86)
		tmp = x + t;
	elseif (z <= -1.62e-285)
		tmp = (y / a) * t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-86], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.62e-285], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000003e-86 or -1.61999999999999994e-285 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 68.3

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

   5. Applied rewrites 68.3%

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

   if -1.60000000000000003e-86 < z < -1.61999999999999994e-285

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 62.4

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

   5. Applied rewrites 62.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 51.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-285}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-86) (+ x t) (if (<= z -1.65e-285) (* (/ t a) y) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-86) {
		tmp = x + t;
	} else if (z <= -1.65e-285) {
		tmp = (t / a) * y;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d-86)) then
        tmp = x + t
    else if (z <= (-1.65d-285)) then
        tmp = (t / a) * y
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-86) {
		tmp = x + t;
	} else if (z <= -1.65e-285) {
		tmp = (t / a) * y;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-86:
		tmp = x + t
	elif z <= -1.65e-285:
		tmp = (t / a) * y
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-86)
		tmp = Float64(x + t);
	elseif (z <= -1.65e-285)
		tmp = Float64(Float64(t / a) * y);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e-86)
		tmp = x + t;
	elseif (z <= -1.65e-285)
		tmp = (t / a) * y;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-86], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.65e-285], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000003e-86 or -1.64999999999999993e-285 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 68.3

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

   5. Applied rewrites 68.3%

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

   if -1.60000000000000003e-86 < z < -1.64999999999999993e-285

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 62.4

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

   5. Applied rewrites 62.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 43.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 6.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + 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 = x + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

Derivation

1. Initial program 80.4%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t + x} \]
4. Step-by-step derivation

   1. lower-+.f64 61.4

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

5. Applied rewrites 61.4%

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

6. Final simplification 61.4%

   \[\leadsto x + t \]
7. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.7× 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 2024264 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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