Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.8% → 97.8%

Time: 5.4s

Alternatives: 9

Speedup: 1.0×

• 25.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (- y x) (/ z t) x))

C

double code(double x, double y, double z, double t) {
	return fma((y - x), (z / t), x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(y - x), Float64(z / t), x)
end

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 97.6%

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

3. Simplified 97.6%

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

Alternative 2: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21} \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+21) (not (<= (/ z t) 0.5))) (- (/ x (/ t z))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+21) || !((z / t) <= 0.5)) {
		tmp = -(x / (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1d+21)) .or. (.not. ((z / t) <= 0.5d0))) then
        tmp = -(x / (t / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+21) || !((z / t) <= 0.5)) {
		tmp = -(x / (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e+21) or not ((z / t) <= 0.5):
		tmp = -(x / (t / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+21) || !(Float64(z / t) <= 0.5))
		tmp = Float64(-Float64(x / Float64(t / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e+21) || ~(((z / t) <= 0.5)))
		tmp = -(x / (t / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+21], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.5]], $MachinePrecision]], (-N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e21 or 0.5 < (/.f64 z t)

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in z around inf 59.7%

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

      1. associate-*r/ 59.7%

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

      2. neg-mul-1 59.7%

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

   8. Simplified 59.7%

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

      1. distribute-frac-neg 59.7%

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

      2. distribute-rgt-neg-out 59.7%

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

      3. clear-num 59.7%

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

      4. add-sqr-sqrt 27.0%

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

      5. sqrt-unprod 30.3%

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

      6. sqr-neg 30.3%

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

      7. sqrt-unprod 3.0%

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

      8. add-sqr-sqrt 8.0%

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

      9. un-div-inv 8.0%

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

      10. add-sqr-sqrt 3.0%

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

      11. sqrt-unprod 29.6%

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

      12. sqr-neg 29.6%

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

      13. sqrt-unprod 26.3%

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

      14. add-sqr-sqrt 59.0%

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

   10. Applied egg-rr 59.0%

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

   if -1e21 < (/.f64 z t) < 0.5

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 72.7%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21} \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;-\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e+21)
   (- (/ x (/ t z)))
   (if (<= (/ z t) 0.5) x (* x (/ (- z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = -(x / (t / z));
	} else if ((z / t) <= 0.5) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d+21)) then
        tmp = -(x / (t / z))
    else if ((z / t) <= 0.5d0) then
        tmp = x
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+21) {
		tmp = -(x / (t / z));
	} else if ((z / t) <= 0.5) {
		tmp = x;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e+21:
		tmp = -(x / (t / z))
	elif (z / t) <= 0.5:
		tmp = x
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e+21)
		tmp = Float64(-Float64(x / Float64(t / z)));
	elseif (Float64(z / t) <= 0.5)
		tmp = x;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e+21)
		tmp = -(x / (t / z));
	elseif ((z / t) <= 0.5)
		tmp = x;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e+21], (-N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(z / t), $MachinePrecision], 0.5], x, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e21

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in z around inf 54.0%

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

      1. associate-*r/ 54.0%

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

      2. neg-mul-1 54.0%

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

   8. Simplified 54.0%

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

      1. distribute-frac-neg 54.0%

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

      2. distribute-rgt-neg-out 54.0%

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

      3. clear-num 54.0%

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

      4. add-sqr-sqrt 24.0%

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

      5. sqrt-unprod 32.3%

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

      6. sqr-neg 32.3%

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

      7. sqrt-unprod 5.3%

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

      8. add-sqr-sqrt 8.6%

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

      9. un-div-inv 8.6%

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

      10. add-sqr-sqrt 5.3%

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

      11. sqrt-unprod 32.3%

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

      12. sqr-neg 32.3%

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

      13. sqrt-unprod 24.1%

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

      14. add-sqr-sqrt 54.0%

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

   10. Applied egg-rr 54.0%

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

   if -1e21 < (/.f64 z t) < 0.5

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 72.7%

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

   if 0.5 < (/.f64 z t)

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in z around inf 65.7%

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

      1. associate-*r/ 65.7%

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

      2. neg-mul-1 65.7%

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

   8. Simplified 65.7%

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

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-28} \lor \neg \left(x \leq 6.6 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-28) (not (<= x 6.6e-22)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-28) || !(x <= 6.6e-22)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.6d-28)) .or. (.not. (x <= 6.6d-22))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-28) || !(x <= 6.6e-22)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-28) or not (x <= 6.6e-22):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-28) || !(x <= 6.6e-22))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e-28) || ~((x <= 6.6e-22)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-28], N[Not[LessEqual[x, 6.6e-22]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999991e-28 or 6.6000000000000002e-22 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. unsub-neg 91.0%

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

   5. Simplified 91.0%

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

   if -1.59999999999999991e-28 < x < 6.6000000000000002e-22

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-*r/ 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-28} \lor \neg \left(x \leq 6.6 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e-31)
   (* x (- 1.0 (/ z t)))
   (if (<= x 7.5e-22) (+ x (* y (/ z t))) (- x (* x (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-31) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 7.5e-22) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7.6d-31)) then
        tmp = x * (1.0d0 - (z / t))
    else if (x <= 7.5d-22) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-31) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 7.5e-22) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e-31:
		tmp = x * (1.0 - (z / t))
	elif x <= 7.5e-22:
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e-31)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	elseif (x <= 7.5e-22)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e-31)
		tmp = x * (1.0 - (z / t));
	elseif (x <= 7.5e-22)
		tmp = x + (y * (z / t));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e-31], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-22], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5999999999999999e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   if -7.5999999999999999e-31 < x < 7.49999999999999978e-22

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-*r/ 88.1%

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

   5. Simplified 88.1%

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

   if 7.49999999999999978e-22 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. associate-/l* 93.8%

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

      3. distribute-lft-neg-out 93.8%

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

      4. *-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+219) (* x (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+219) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d+219)) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+219) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+219:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+219)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+219)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+219], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.99999999999999993e219

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. unsub-neg 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around inf 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   8. Simplified 52.5%

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

      1. *-commutative 52.5%

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

      2. associate-*l/ 49.4%

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

      3. distribute-lft-neg-in 49.4%

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

      4. distribute-rgt-neg-out 49.4%

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

      5. expm1-log1p-u 26.6%

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

      6. expm1-undefine 26.6%

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

      7. distribute-rgt-neg-out 26.6%

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

      8. distribute-lft-neg-in 26.6%

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

      9. associate-*l/ 29.6%

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

      10. *-commutative 29.6%

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

      11. clear-num 29.6%

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

      12. un-div-inv 29.6%

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

      13. add-sqr-sqrt 23.0%

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

      14. sqrt-unprod 25.9%

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

      15. sqr-neg 25.9%

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

      16. sqrt-unprod 0.1%

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

      17. add-sqr-sqrt 10.2%

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

   10. Applied egg-rr 10.2%

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

       1. sub-neg 10.2%

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

       2. metadata-eval 10.2%

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

       3. +-commutative 10.2%

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

       4. log1p-undefine 10.2%

          \[\leadsto -1 + e^{\color{blue}{\log \left(1 + \frac{x}{\frac{t}{z}}\right)}} \]

       5. rem-exp-log 17.2%

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

       6. associate-+r+ 17.2%

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

       7. metadata-eval 17.2%

          \[\leadsto \color{blue}{0} + \frac{x}{\frac{t}{z}} \]

       8. rem-square-sqrt 10.2%

          \[\leadsto 0 + \color{blue}{\sqrt{\frac{x}{\frac{t}{z}}} \cdot \sqrt{\frac{x}{\frac{t}{z}}}} \]

       9. cancel-sign-sub 10.2%

          \[\leadsto \color{blue}{0 - \left(-\sqrt{\frac{x}{\frac{t}{z}}}\right) \cdot \sqrt{\frac{x}{\frac{t}{z}}}} \]

       10. neg-sub0 10.2%

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

       11. distribute-lft-neg-in 10.2%

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

       12. remove-double-neg 10.2%

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

       13. rem-square-sqrt 17.2%

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

       14. associate-/r/ 8.3%

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

       15. associate-*l/ 8.3%

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

       16. associate-*r/ 17.2%

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

   12. Simplified 17.2%

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

   if -1.99999999999999993e219 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 41.1%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

Alternative 8: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in x around inf 66.4%

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

   1. mul-1-neg 66.4%

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

   2. unsub-neg 66.4%

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

5. Simplified 66.4%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
6. Add Preprocessing

Alternative 9: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in z around 0 36.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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