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

Percentage Accurate: 85.8% → 95.3%

Time: 7.8s

Alternatives: 11

Speedup: 0.8×

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: 85.8% 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: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{y - z}{\frac{a - z}{t}} + x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.1%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.9

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

4. Applied rewrites 97.9%

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

5. Final simplification 97.9%

   \[\leadsto \frac{y - z}{\frac{a - z}{t}} + x \]
6. Add Preprocessing

Alternative 2: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y z)) (- a z))))
   (if (<= t_1 (- INFINITY))
     (fma (- 1.0 (/ y z)) t x)
     (if (<= t_1 5e+277) (+ t_1 x) (/ (- y z) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else if (t_1 <= 5e+277) {
		tmp = t_1 + x;
	} else {
		tmp = (y - z) / ((a - z) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	elseif (t_1 <= 5e+277)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(Float64(y - z) / Float64(Float64(a - z) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+277], N[(t$95$1 + x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 31.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 83.2

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

   5. Applied rewrites 83.2%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999982e277

   1. Initial program 99.8%

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

   if 4.99999999999999982e277 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 32.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 93.4

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

   5. Applied rewrites 93.4%

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

   7. Applied rewrites 93.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+266}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y z)) (- a z))))
   (if (<= t_1 (- INFINITY))
     (fma (- 1.0 (/ y z)) t x)
     (if (<= t_1 5e+266) (+ t_1 x) (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else if (t_1 <= 5e+266) {
		tmp = t_1 + x;
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	elseif (t_1 <= 5e+266)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+266], N[(t$95$1 + x), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 31.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 83.2

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

   5. Applied rewrites 83.2%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.9999999999999999e266

   1. Initial program 99.8%

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

   if 4.9999999999999999e266 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 35.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 90.8

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

   5. Applied rewrites 90.8%

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

   7. Applied rewrites 90.9%

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

   9. Applied rewrites 93.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+266}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y z)) (- a z))))
   (if (<= t_1 (- INFINITY))
     (fma (- 1.0 (/ y z)) t x)
     (if (<= t_1 5e+277) (+ t_1 x) (* (/ t (- a z)) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else if (t_1 <= 5e+277) {
		tmp = t_1 + x;
	} else {
		tmp = (t / (a - z)) * (y - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	elseif (t_1 <= 5e+277)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+277], N[(t$95$1 + x), $MachinePrecision], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 31.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 83.2

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

   5. Applied rewrites 83.2%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999982e277

   1. Initial program 99.8%

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

   if 4.99999999999999982e277 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 32.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 93.4

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

   5. Applied rewrites 93.4%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e+37)
     t_1
     (if (<= t_2 5e+68) (fma (- t) (/ z (- a z)) x) 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 <= -1e+37) {
		tmp = t_1;
	} else if (t_2 <= 5e+68) {
		tmp = fma(-t, (z / (a - z)), x);
	} 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 <= -1e+37)
		tmp = t_1;
	elseif (t_2 <= 5e+68)
		tmp = fma(Float64(-t), Float64(z / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return 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, -1e+37], t$95$1, If[LessEqual[t$95$2, 5e+68], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -9.99999999999999954e36 or 5.0000000000000004e68 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 62.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 80.8

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

   5. Applied rewrites 80.8%

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

   if -9.99999999999999954e36 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.0000000000000004e68

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 91.0

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

   5. Applied rewrites 91.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t) (/ z (- a z)) x)))
   (if (<= z -0.55) t_1 (if (<= z 2.5e+22) (+ (/ (* t y) (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-t, (z / (a - z)), x);
	double tmp;
	if (z <= -0.55) {
		tmp = t_1;
	} else if (z <= 2.5e+22) {
		tmp = ((t * y) / (a - z)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(-t), Float64(z / Float64(a - z)), x)
	tmp = 0.0
	if (z <= -0.55)
		tmp = t_1;
	elseif (z <= 2.5e+22)
		tmp = Float64(Float64(Float64(t * y) / Float64(a - z)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -0.55], t$95$1, If[LessEqual[z, 2.5e+22], N[(N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.55000000000000004 or 2.4999999999999998e22 < z

   1. Initial program 67.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 90.5

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

   5. Applied rewrites 90.5%

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

   if -0.55000000000000004 < z < 2.4999999999999998e22

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.9

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

   5. Applied rewrites 85.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ y z)) t x)))
   (if (<= z -2.7e-34) t_1 (if (<= z 1.46e-33) (fma y (/ t a) 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 <= -2.7e-34) {
		tmp = t_1;
	} else if (z <= 1.46e-33) {
		tmp = fma(y, (t / a), 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 <= -2.7e-34)
		tmp = t_1;
	elseif (z <= 1.46e-33)
		tmp = fma(y, Float64(t / a), 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, -2.7e-34], t$95$1, If[LessEqual[z, 1.46e-33], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000017e-34 or 1.45999999999999999e-33 < z

   1. Initial program 70.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 86.5

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

   5. Applied rewrites 86.5%

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

   if -2.70000000000000017e-34 < z < 1.45999999999999999e-33

   1. Initial program 94.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 79.1

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

   7. Applied rewrites 79.1%

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

Alternative 8: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e-9) (+ t x) (if (<= z 1.46e-33) (fma y (/ t a) x) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e-9) {
		tmp = t + x;
	} else if (z <= 1.46e-33) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e-9)
		tmp = Float64(t + x);
	elseif (z <= 1.46e-33)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(t + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e-9], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.46e-33], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999982e-9 or 1.45999999999999999e-33 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if -5.79999999999999982e-9 < z < 1.45999999999999999e-33

   1. Initial program 94.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 79.1

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

   7. Applied rewrites 79.1%

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

Alternative 9: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e-9) (+ t x) (if (<= z 1.46e-33) (fma (/ y a) t x) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e-9) {
		tmp = t + x;
	} else if (z <= 1.46e-33) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e-9)
		tmp = Float64(t + x);
	elseif (z <= 1.46e-33)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(t + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e-9], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.46e-33], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999982e-9 or 1.45999999999999999e-33 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if -5.79999999999999982e-9 < z < 1.45999999999999999e-33

   1. Initial program 94.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 75.6

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

   5. Applied rewrites 75.6%

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

Alternative 10: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-209}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{-165}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e-209) (+ t x) (if (<= z 1.86e-165) (* (/ t a) y) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e-209) {
		tmp = t + x;
	} else if (z <= 1.86e-165) {
		tmp = (t / a) * y;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d-209)) then
        tmp = t + x
    else if (z <= 1.86d-165) then
        tmp = (t / a) * y
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e-209) {
		tmp = t + x;
	} else if (z <= 1.86e-165) {
		tmp = (t / a) * y;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e-209:
		tmp = t + x
	elif z <= 1.86e-165:
		tmp = (t / a) * y
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e-209)
		tmp = Float64(t + x);
	elseif (z <= 1.86e-165)
		tmp = Float64(Float64(t / a) * y);
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e-209)
		tmp = t + x;
	elseif (z <= 1.86e-165)
		tmp = (t / a) * y;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e-209], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.86e-165], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999996e-209 or 1.86000000000000002e-165 < z

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 70.4

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

   5. Applied rewrites 70.4%

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

   if -2.09999999999999996e-209 < z < 1.86000000000000002e-165

   1. Initial program 91.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 62.2

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 47.6%

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

   10. Applied rewrites 53.9%

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

Alternative 11: 60.1% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.1%

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

3. Taylor expanded in z around inf

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

   1. lower-+.f64 61.7

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

5. Applied rewrites 61.7%

   \[\leadsto \color{blue}{t + x} \]
6. Add Preprocessing

Developer Target 1: 99.0% 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 2024244 
(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))))