Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.7% → 97.5%

Time: 9.8s

Alternatives: 9

Speedup: 1.1×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 97.8

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

4. Applied egg-rr 97.8%

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

Alternative 2: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-52}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma z (/ y t) x)))
   (if (<= t -7.5e+60) t_1 (if (<= t 3.05e-52) (/ (* z (- y x)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, (y / t), x);
	double tmp;
	if (t <= -7.5e+60) {
		tmp = t_1;
	} else if (t <= 3.05e-52) {
		tmp = (z * (y - x)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(z, Float64(y / t), x)
	tmp = 0.0
	if (t <= -7.5e+60)
		tmp = t_1;
	elseif (t <= 3.05e-52)
		tmp = Float64(Float64(z * Float64(y - x)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -7.5e+60], t$95$1, If[LessEqual[t, 3.05e-52], N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e60 or 3.04999999999999995e-52 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 81.3%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 89.5

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

   7. Applied egg-rr 89.5%

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

   if -7.5e60 < t < 3.04999999999999995e-52

   1. Initial program 99.3%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 97.2

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 86.4

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

   7. Simplified 86.4%

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

Alternative 3: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= z -1.16e+40) t_1 (if (<= z 6.2e-30) (+ x (/ (* z y) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if (z <= -1.16e+40) {
		tmp = t_1;
	} else if (z <= 6.2e-30) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = z * ((y - x) / t)
    if (z <= (-1.16d+40)) then
        tmp = t_1
    else if (z <= 6.2d-30) then
        tmp = x + ((z * y) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if (z <= -1.16e+40) {
		tmp = t_1;
	} else if (z <= 6.2e-30) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if z <= -1.16e+40:
		tmp = t_1
	elif z <= 6.2e-30:
		tmp = x + ((z * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (z <= -1.16e+40)
		tmp = t_1;
	elseif (z <= 6.2e-30)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if (z <= -1.16e+40)
		tmp = t_1;
	elseif (z <= 6.2e-30)
		tmp = x + ((z * y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+40], t$95$1, If[LessEqual[z, 6.2e-30], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.16000000000000012e40 or 6.19999999999999982e-30 < z

   1. Initial program 87.2%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 97.1

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 77.2

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

   7. Simplified 77.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. div-inv N/A

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

      4. remove-double-div N/A

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

      5. inv-pow N/A

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

      6. inv-pow N/A

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

      7. pow-prod-down N/A

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

      8. *-commutative N/A

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

      9. pow-prod-down N/A

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

      10. inv-pow N/A

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

      11. inv-pow N/A

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

      12. remove-double-div N/A

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

      13. *-lowering-*.f64 N/A

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

      14. inv-pow N/A

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

      15. remove-double-div N/A

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

      16. inv-pow N/A

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

      17. pow-prod-down N/A

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

      18. *-commutative N/A

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

      19. pow-prod-down N/A

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

      20. inv-pow N/A

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

      21. remove-double-div N/A

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

      22. inv-pow N/A

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

      23. div-inv N/A

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

      24. /-lowering-/.f64 N/A

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

      25. --lowering--.f64 86.5

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

   9. Applied egg-rr 86.5%

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

   if -1.16000000000000012e40 < z < 6.19999999999999982e-30

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 88.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) y x)))
   (if (<= y -1.1e-64) t_1 (if (<= y 2.1e-135) (* x (- 1.0 (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z / t), y, x);
	double tmp;
	if (y <= -1.1e-64) {
		tmp = t_1;
	} else if (y <= 2.1e-135) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z / t), y, x)
	tmp = 0.0
	if (y <= -1.1e-64)
		tmp = t_1;
	elseif (y <= 2.1e-135)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[y, -1.1e-64], t$95$1, If[LessEqual[y, 2.1e-135], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e-64 or 2.1e-135 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 80.9%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 85.0

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

   7. Applied egg-rr 85.0%

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

   if -1.1e-64 < y < 2.1e-135

   1. Initial program 95.2%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 97.6

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-rgt-identity N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 93.2

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

   7. Simplified 93.2%

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

Alternative 5: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma z (/ y t) x)))
   (if (<= t -2.7e-200) t_1 (if (<= t 7.5e-101) (* (/ z t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, (y / t), x);
	double tmp;
	if (t <= -2.7e-200) {
		tmp = t_1;
	} else if (t <= 7.5e-101) {
		tmp = (z / t) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(z, Float64(y / t), x)
	tmp = 0.0
	if (t <= -2.7e-200)
		tmp = t_1;
	elseif (t <= 7.5e-101)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.7e-200], t$95$1, If[LessEqual[t, 7.5e-101], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7000000000000001e-200 or 7.5000000000000001e-101 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 74.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 78.4

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

   7. Applied egg-rr 78.4%

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

   if -2.7000000000000001e-200 < t < 7.5000000000000001e-101

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 51.3

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

   5. Simplified 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \frac{y}{t}, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. associate-*r/ N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 70.2

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

   7. Applied egg-rr 70.2%

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

Alternative 6: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+52}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.65e+45) x (if (<= t 1.55e+52) (* (/ z t) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.65e+45) {
		tmp = x;
	} else if (t <= 1.55e+52) {
		tmp = (z / t) * y;
	} 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 (t <= (-2.65d+45)) then
        tmp = x
    else if (t <= 1.55d+52) then
        tmp = (z / t) * y
    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 (t <= -2.65e+45) {
		tmp = x;
	} else if (t <= 1.55e+52) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.65e+45:
		tmp = x
	elif t <= 1.55e+52:
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.65e+45)
		tmp = x;
	elseif (t <= 1.55e+52)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.65e+45)
		tmp = x;
	elseif (t <= 1.55e+52)
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.65e+45], x, If[LessEqual[t, 1.55e+52], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.64999999999999996e45 or 1.55e52 < t

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 68.8%

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

   if -2.64999999999999996e45 < t < 1.55e52

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 45.9

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

   5. Simplified 45.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \frac{y}{t}, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. associate-*r/ N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 54.3

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

   7. Applied egg-rr 54.3%

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

Alternative 7: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8200000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= z -1.2e-30) t_1 (if (<= z 8200000000.0) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -1.2e-30) {
		tmp = t_1;
	} else if (z <= 8200000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = z * (y / t)
    if (z <= (-1.2d-30)) then
        tmp = t_1
    else if (z <= 8200000000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -1.2e-30) {
		tmp = t_1;
	} else if (z <= 8200000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if z <= -1.2e-30:
		tmp = t_1
	elif z <= 8200000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (z <= -1.2e-30)
		tmp = t_1;
	elseif (z <= 8200000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (z <= -1.2e-30)
		tmp = t_1;
	elseif (z <= 8200000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-30], t$95$1, If[LessEqual[z, 8200000000.0], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999992e-30 or 8.2e9 < z

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0

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

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 54.3

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

   5. Simplified 54.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \frac{y}{t}, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 54.3

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

   7. Applied egg-rr 54.3%

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

   if -1.19999999999999992e-30 < z < 8.2e9

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 60.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8200000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.4%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. /-lowering-/.f64 77.1

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

7. Applied egg-rr 77.1%

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

Alternative 9: 38.8% accurate, 23.0× 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 93.0%

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

3. Taylor expanded in z around 0

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

5. Simplified 37.3%

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

Developer Target 1: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	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 < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

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