Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 8

Speedup: 0.1×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right) + t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (fma (* z -0.5) y (* 0.125 x)) t))

C

double code(double x, double y, double z, double t) {
	return fma((z * -0.5), y, (0.125 * x)) + t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(z * -0.5), y, Float64(0.125 * x)) + t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z * -0.5), $MachinePrecision] * y + N[(0.125 * x), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

   2. +-commutative 100.0%

      \[\leadsto \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]

   3. associate-/l* 99.9%

      \[\leadsto \left(\left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + \frac{1}{8} \cdot x\right) + t \]

   4. distribute-frac-neg 99.9%

      \[\leadsto \left(\color{blue}{\frac{-y}{\frac{2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

   5. metadata-eval 99.9%

      \[\leadsto \left(\frac{-y}{\frac{\color{blue}{--2}}{z}} + \frac{1}{8} \cdot x\right) + t \]

   6. distribute-neg-frac 99.9%

      \[\leadsto \left(\frac{-y}{\color{blue}{-\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

   7. frac-2neg 99.9%

      \[\leadsto \left(\color{blue}{\frac{y}{\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

   8. clear-num 99.8%

      \[\leadsto \left(\color{blue}{\frac{1}{\frac{\frac{-2}{z}}{y}}} + \frac{1}{8} \cdot x\right) + t \]

   9. associate-/r/ 99.9%

      \[\leadsto \left(\color{blue}{\frac{1}{\frac{-2}{z}} \cdot y} + \frac{1}{8} \cdot x\right) + t \]

   10. clear-num 100.0%

       \[\leadsto \left(\color{blue}{\frac{z}{-2}} \cdot y + \frac{1}{8} \cdot x\right) + t \]

   11. fma-def 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-2}, y, \frac{1}{8} \cdot x\right)} + t \]

   12. div-inv 100.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \frac{1}{-2}}, y, \frac{1}{8} \cdot x\right) + t \]

   13. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{-0.5}, y, \frac{1}{8} \cdot x\right) + t \]

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, \color{blue}{0.125} \cdot x\right) + t \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right)} + t \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right) + t \]

Alternative 2: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.5 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \cdot y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot y \leq -9.5 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 1.3 \cdot 10^{-245}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \cdot y \leq 1.4 \cdot 10^{-58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 5000000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.5 (* z y))))
   (if (<= (* z y) -2.5e-10)
     t_1
     (if (<= (* z y) -9.5e-308)
       t
       (if (<= (* z y) 1.3e-245)
         (* 0.125 x)
         (if (<= (* z y) 1.4e-58)
           t
           (if (<= (* z y) 5000000000.0) (* 0.125 x) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (z * y);
	double tmp;
	if ((z * y) <= -2.5e-10) {
		tmp = t_1;
	} else if ((z * y) <= -9.5e-308) {
		tmp = t;
	} else if ((z * y) <= 1.3e-245) {
		tmp = 0.125 * x;
	} else if ((z * y) <= 1.4e-58) {
		tmp = t;
	} else if ((z * y) <= 5000000000.0) {
		tmp = 0.125 * 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 = (-0.5d0) * (z * y)
    if ((z * y) <= (-2.5d-10)) then
        tmp = t_1
    else if ((z * y) <= (-9.5d-308)) then
        tmp = t
    else if ((z * y) <= 1.3d-245) then
        tmp = 0.125d0 * x
    else if ((z * y) <= 1.4d-58) then
        tmp = t
    else if ((z * y) <= 5000000000.0d0) then
        tmp = 0.125d0 * 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 = -0.5 * (z * y);
	double tmp;
	if ((z * y) <= -2.5e-10) {
		tmp = t_1;
	} else if ((z * y) <= -9.5e-308) {
		tmp = t;
	} else if ((z * y) <= 1.3e-245) {
		tmp = 0.125 * x;
	} else if ((z * y) <= 1.4e-58) {
		tmp = t;
	} else if ((z * y) <= 5000000000.0) {
		tmp = 0.125 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 * (z * y)
	tmp = 0
	if (z * y) <= -2.5e-10:
		tmp = t_1
	elif (z * y) <= -9.5e-308:
		tmp = t
	elif (z * y) <= 1.3e-245:
		tmp = 0.125 * x
	elif (z * y) <= 1.4e-58:
		tmp = t
	elif (z * y) <= 5000000000.0:
		tmp = 0.125 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(z * y))
	tmp = 0.0
	if (Float64(z * y) <= -2.5e-10)
		tmp = t_1;
	elseif (Float64(z * y) <= -9.5e-308)
		tmp = t;
	elseif (Float64(z * y) <= 1.3e-245)
		tmp = Float64(0.125 * x);
	elseif (Float64(z * y) <= 1.4e-58)
		tmp = t;
	elseif (Float64(z * y) <= 5000000000.0)
		tmp = Float64(0.125 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 * (z * y);
	tmp = 0.0;
	if ((z * y) <= -2.5e-10)
		tmp = t_1;
	elseif ((z * y) <= -9.5e-308)
		tmp = t;
	elseif ((z * y) <= 1.3e-245)
		tmp = 0.125 * x;
	elseif ((z * y) <= 1.4e-58)
		tmp = t;
	elseif ((z * y) <= 5000000000.0)
		tmp = 0.125 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -2.5e-10], t$95$1, If[LessEqual[N[(z * y), $MachinePrecision], -9.5e-308], t, If[LessEqual[N[(z * y), $MachinePrecision], 1.3e-245], N[(0.125 * x), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 1.4e-58], t, If[LessEqual[N[(z * y), $MachinePrecision], 5000000000.0], N[(0.125 * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2.50000000000000016e-10 or 5e9 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]

      3. associate-/l* 99.8%

         \[\leadsto \left(\left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + \frac{1}{8} \cdot x\right) + t \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{-y}{\frac{2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      5. metadata-eval 99.8%

         \[\leadsto \left(\frac{-y}{\frac{\color{blue}{--2}}{z}} + \frac{1}{8} \cdot x\right) + t \]

      6. distribute-neg-frac 99.8%

         \[\leadsto \left(\frac{-y}{\color{blue}{-\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      7. frac-2neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{y}{\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      8. clear-num 99.7%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{\frac{-2}{z}}{y}}} + \frac{1}{8} \cdot x\right) + t \]

      9. associate-/r/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{-2}{z}} \cdot y} + \frac{1}{8} \cdot x\right) + t \]

      10. clear-num 100.0%

          \[\leadsto \left(\color{blue}{\frac{z}{-2}} \cdot y + \frac{1}{8} \cdot x\right) + t \]

      11. fma-def 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-2}, y, \frac{1}{8} \cdot x\right)} + t \]

      12. div-inv 100.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \frac{1}{-2}}, y, \frac{1}{8} \cdot x\right) + t \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{-0.5}, y, \frac{1}{8} \cdot x\right) + t \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, \color{blue}{0.125} \cdot x\right) + t \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right)} + t \]

   4. Taylor expanded in z around inf 69.5%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

   if -2.50000000000000016e-10 < (*.f64 y z) < -9.49999999999999963e-308 or 1.30000000000000003e-245 < (*.f64 y z) < 1.4e-58

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in t around inf 62.3%

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

   if -9.49999999999999963e-308 < (*.f64 y z) < 1.30000000000000003e-245 or 1.4e-58 < (*.f64 y z) < 5e9

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]

      3. associate-/l* 100.0%

         \[\leadsto \left(\left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + \frac{1}{8} \cdot x\right) + t \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(\color{blue}{\frac{-y}{\frac{2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      5. metadata-eval 100.0%

         \[\leadsto \left(\frac{-y}{\frac{\color{blue}{--2}}{z}} + \frac{1}{8} \cdot x\right) + t \]

      6. distribute-neg-frac 100.0%

         \[\leadsto \left(\frac{-y}{\color{blue}{-\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      7. frac-2neg 100.0%

         \[\leadsto \left(\color{blue}{\frac{y}{\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      8. clear-num 100.0%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{\frac{-2}{z}}{y}}} + \frac{1}{8} \cdot x\right) + t \]

      9. associate-/r/ 100.0%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{-2}{z}} \cdot y} + \frac{1}{8} \cdot x\right) + t \]

      10. clear-num 100.0%

          \[\leadsto \left(\color{blue}{\frac{z}{-2}} \cdot y + \frac{1}{8} \cdot x\right) + t \]

      11. fma-def 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-2}, y, \frac{1}{8} \cdot x\right)} + t \]

      12. div-inv 100.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \frac{1}{-2}}, y, \frac{1}{8} \cdot x\right) + t \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{-0.5}, y, \frac{1}{8} \cdot x\right) + t \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, \color{blue}{0.125} \cdot x\right) + t \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right)} + t \]

   4. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{0.125 \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq -9.5 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 1.3 \cdot 10^{-245}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \cdot y \leq 1.4 \cdot 10^{-58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \cdot y \leq 5000000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{-16}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (* z y))))
   (if (<= (* z y) -5e-10)
     (- t t_1)
     (if (<= (* z y) 5e-16) (+ (* 0.125 x) t) (- (* 0.125 x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (z * y);
	double tmp;
	if ((z * y) <= -5e-10) {
		tmp = t - t_1;
	} else if ((z * y) <= 5e-16) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = (0.125 * x) - 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 = 0.5d0 * (z * y)
    if ((z * y) <= (-5d-10)) then
        tmp = t - t_1
    else if ((z * y) <= 5d-16) then
        tmp = (0.125d0 * x) + t
    else
        tmp = (0.125d0 * x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (z * y);
	double tmp;
	if ((z * y) <= -5e-10) {
		tmp = t - t_1;
	} else if ((z * y) <= 5e-16) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = (0.125 * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * (z * y)
	tmp = 0
	if (z * y) <= -5e-10:
		tmp = t - t_1
	elif (z * y) <= 5e-16:
		tmp = (0.125 * x) + t
	else:
		tmp = (0.125 * x) - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(z * y))
	tmp = 0.0
	if (Float64(z * y) <= -5e-10)
		tmp = Float64(t - t_1);
	elseif (Float64(z * y) <= 5e-16)
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(Float64(0.125 * x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * (z * y);
	tmp = 0.0;
	if ((z * y) <= -5e-10)
		tmp = t - t_1;
	elseif ((z * y) <= 5e-16)
		tmp = (0.125 * x) + t;
	else
		tmp = (0.125 * x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -5e-10], N[(t - t$95$1), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 5e-16], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000031e-10

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around 0 89.9%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]

   if -5.00000000000000031e-10 < (*.f64 y z) < 5.0000000000000004e-16

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around inf 96.3%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]

   if 5.0000000000000004e-16 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in t around 0 85.4%

      \[\leadsto \color{blue}{0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t - 0.5 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{-16}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - 0.5 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 4: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{-10} \lor \neg \left(z \cdot y \leq 20000000\right):\\ \;\;\;\;t - 0.5 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z y) -5e-10) (not (<= (* z y) 20000000.0)))
   (- t (* 0.5 (* z y)))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -5e-10) || !((z * y) <= 20000000.0)) {
		tmp = t - (0.5 * (z * y));
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * y) <= (-5d-10)) .or. (.not. ((z * y) <= 20000000.0d0))) then
        tmp = t - (0.5d0 * (z * y))
    else
        tmp = (0.125d0 * x) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -5e-10) || !((z * y) <= 20000000.0)) {
		tmp = t - (0.5 * (z * y));
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) <= -5e-10) or not ((z * y) <= 20000000.0):
		tmp = t - (0.5 * (z * y))
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * y) <= -5e-10) || !(Float64(z * y) <= 20000000.0))
		tmp = Float64(t - Float64(0.5 * Float64(z * y)));
	else
		tmp = Float64(Float64(0.125 * x) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * y) <= -5e-10) || ~(((z * y) <= 20000000.0)))
		tmp = t - (0.5 * (z * y));
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * y), $MachinePrecision], -5e-10], N[Not[LessEqual[N[(z * y), $MachinePrecision], 20000000.0]], $MachinePrecision]], N[(t - N[(0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000031e-10 or 2e7 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around 0 85.6%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]

   if -5.00000000000000031e-10 < (*.f64 y z) < 2e7

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around inf 96.4%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5 \cdot 10^{-10} \lor \neg \left(z \cdot y \leq 20000000\right):\\ \;\;\;\;t - 0.5 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 5: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+26} \lor \neg \left(z \cdot y \leq 5 \cdot 10^{+172}\right):\\ \;\;\;\;-0.5 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z y) -2e+26) (not (<= (* z y) 5e+172)))
   (* -0.5 (* z y))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -2e+26) || !((z * y) <= 5e+172)) {
		tmp = -0.5 * (z * y);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * y) <= (-2d+26)) .or. (.not. ((z * y) <= 5d+172))) then
        tmp = (-0.5d0) * (z * y)
    else
        tmp = (0.125d0 * x) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -2e+26) || !((z * y) <= 5e+172)) {
		tmp = -0.5 * (z * y);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) <= -2e+26) or not ((z * y) <= 5e+172):
		tmp = -0.5 * (z * y)
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * y) <= -2e+26) || !(Float64(z * y) <= 5e+172))
		tmp = Float64(-0.5 * Float64(z * y));
	else
		tmp = Float64(Float64(0.125 * x) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * y) <= -2e+26) || ~(((z * y) <= 5e+172)))
		tmp = -0.5 * (z * y);
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * y), $MachinePrecision], -2e+26], N[Not[LessEqual[N[(z * y), $MachinePrecision], 5e+172]], $MachinePrecision]], N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.0000000000000001e26 or 5.0000000000000001e172 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]

      3. associate-/l* 99.8%

         \[\leadsto \left(\left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + \frac{1}{8} \cdot x\right) + t \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{-y}{\frac{2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      5. metadata-eval 99.8%

         \[\leadsto \left(\frac{-y}{\frac{\color{blue}{--2}}{z}} + \frac{1}{8} \cdot x\right) + t \]

      6. distribute-neg-frac 99.8%

         \[\leadsto \left(\frac{-y}{\color{blue}{-\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      7. frac-2neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{y}{\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      8. clear-num 99.7%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{\frac{-2}{z}}{y}}} + \frac{1}{8} \cdot x\right) + t \]

      9. associate-/r/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{-2}{z}} \cdot y} + \frac{1}{8} \cdot x\right) + t \]

      10. clear-num 100.0%

          \[\leadsto \left(\color{blue}{\frac{z}{-2}} \cdot y + \frac{1}{8} \cdot x\right) + t \]

      11. fma-def 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-2}, y, \frac{1}{8} \cdot x\right)} + t \]

      12. div-inv 100.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \frac{1}{-2}}, y, \frac{1}{8} \cdot x\right) + t \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{-0.5}, y, \frac{1}{8} \cdot x\right) + t \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, \color{blue}{0.125} \cdot x\right) + t \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right)} + t \]

   4. Taylor expanded in z around inf 80.7%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

   if -2.0000000000000001e26 < (*.f64 y z) < 5.0000000000000001e172

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around inf 85.9%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -2 \cdot 10^{+26} \lor \neg \left(z \cdot y \leq 5 \cdot 10^{+172}\right):\\ \;\;\;\;-0.5 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(0.125 \cdot x + t\right) - y \cdot \left(z \cdot 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ (* 0.125 x) t) (* y (* z 0.5))))

C

double code(double x, double y, double z, double t) {
	return ((0.125 * x) + t) - (y * (z * 0.5));
}

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 = ((0.125d0 * x) + t) - (y * (z * 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((0.125 * x) + t) - (y * (z * 0.5));
}

Python

def code(x, y, z, t):
	return ((0.125 * x) + t) - (y * (z * 0.5))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(0.125 * x) + t) - Float64(y * Float64(z * 0.5)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((0.125 * x) + t) - (y * (z * 0.5));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision] - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{t + \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right)} \]

   2. associate-+r- 100.0%

      \[\leadsto \color{blue}{\left(t + \frac{1}{8} \cdot x\right) - \frac{y \cdot z}{2}} \]

   3. metadata-eval 100.0%

      \[\leadsto \left(t + \color{blue}{0.125} \cdot x\right) - \frac{y \cdot z}{2} \]

   4. div-inv 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - \color{blue}{\left(y \cdot z\right) \cdot \frac{1}{2}} \]

   5. associate-*l* 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - \color{blue}{y \cdot \left(z \cdot \frac{1}{2}\right)} \]

   6. metadata-eval 100.0%

      \[\leadsto \left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot \color{blue}{0.5}\right) \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - y \cdot \left(z \cdot 0.5\right)} \]

4. Final simplification 100.0%

   \[\leadsto \left(0.125 \cdot x + t\right) - y \cdot \left(z \cdot 0.5\right) \]

Alternative 7: 49.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+33}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.6e+36) t (if (<= t 9e+33) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.6e+36) {
		tmp = t;
	} else if (t <= 9e+33) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7.6d+36)) then
        tmp = t
    else if (t <= 9d+33) then
        tmp = 0.125d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.6e+36) {
		tmp = t;
	} else if (t <= 9e+33) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.6e+36:
		tmp = t
	elif t <= 9e+33:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.6e+36)
		tmp = t;
	elseif (t <= 9e+33)
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.6e+36)
		tmp = t;
	elseif (t <= 9e+33)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.6e+36], t, If[LessEqual[t, 9e+33], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -7.6000000000000005e36 or 9.0000000000000001e33 < t

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in t around inf 67.2%

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

   if -7.6000000000000005e36 < t < 9.0000000000000001e33

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]

      3. associate-/l* 99.8%

         \[\leadsto \left(\left(-\color{blue}{\frac{y}{\frac{2}{z}}}\right) + \frac{1}{8} \cdot x\right) + t \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{-y}{\frac{2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      5. metadata-eval 99.8%

         \[\leadsto \left(\frac{-y}{\frac{\color{blue}{--2}}{z}} + \frac{1}{8} \cdot x\right) + t \]

      6. distribute-neg-frac 99.8%

         \[\leadsto \left(\frac{-y}{\color{blue}{-\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      7. frac-2neg 99.8%

         \[\leadsto \left(\color{blue}{\frac{y}{\frac{-2}{z}}} + \frac{1}{8} \cdot x\right) + t \]

      8. clear-num 99.7%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{\frac{-2}{z}}{y}}} + \frac{1}{8} \cdot x\right) + t \]

      9. associate-/r/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1}{\frac{-2}{z}} \cdot y} + \frac{1}{8} \cdot x\right) + t \]

      10. clear-num 100.0%

          \[\leadsto \left(\color{blue}{\frac{z}{-2}} \cdot y + \frac{1}{8} \cdot x\right) + t \]

      11. fma-def 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{-2}, y, \frac{1}{8} \cdot x\right)} + t \]

      12. div-inv 100.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \frac{1}{-2}}, y, \frac{1}{8} \cdot x\right) + t \]

      13. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{-0.5}, y, \frac{1}{8} \cdot x\right) + t \]

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z \cdot -0.5, y, \color{blue}{0.125} \cdot x\right) + t \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, 0.125 \cdot x\right)} + t \]

   4. Taylor expanded in x around inf 40.4%

      \[\leadsto \color{blue}{0.125 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+33}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 32.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

2. Taylor expanded in t around inf 35.5%

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

3. Final simplification 35.5%

   \[\leadsto t \]

Developer target: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ (/ x 8.0) t) (* (/ z 2.0) y)))

C

double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

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 / 8.0d0) + t) - ((z / 2.0d0) * y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

Python

def code(x, y, z, t):
	return ((x / 8.0) + t) - ((z / 2.0) * y)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / 8.0) + t) - Float64(Float64(z / 2.0) * y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / 8.0) + t) - ((z / 2.0) * y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / 8.0), $MachinePrecision] + t), $MachinePrecision] - N[(N[(z / 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))