Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.6% → 89.3%

Time: 13.4s

Alternatives: 18

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (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 - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (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 - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x \cdot \left(y - a\right)}{z \cdot t}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-219)
     t_1
     (if (<= t_2 2e-284) (fma t (/ (* x (- y a)) (* z t)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -2e-219) {
		tmp = t_1;
	} else if (t_2 <= 2e-284) {
		tmp = fma(t, ((x * (y - a)) / (z * t)), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-219)
		tmp = t_1;
	elseif (t_2 <= 2e-284)
		tmp = fma(t, Float64(Float64(x * Float64(y - a)) / Float64(z * t)), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-219], t$95$1, If[LessEqual[t$95$2, 2e-284], N[(t * N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.0000000000000001e-219 or 2.00000000000000007e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 88.7

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

   4. Applied egg-rr 88.7%

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

   if -2.0000000000000001e-219 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000007e-284

   1. Initial program 6.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 96.6%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 96.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-*l/ N/A

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

      4. div-inv N/A

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

      5. times-frac N/A

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

      6. flip3-- N/A

         \[\leadsto \frac{1}{z} \cdot \frac{x}{\frac{1}{\color{blue}{\frac{{y}^{3} - {a}^{3}}{y \cdot y + \left(a \cdot a + y \cdot a\right)}}}} + t \]

      7. clear-num N/A

         \[\leadsto \frac{1}{z} \cdot \frac{x}{\color{blue}{\frac{y \cdot y + \left(a \cdot a + y \cdot a\right)}{{y}^{3} - {a}^{3}}}} + t \]

      8. un-div-inv N/A

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{y \cdot y + \left(a \cdot a + y \cdot a\right)}{{y}^{3} - {a}^{3}}}\right)} + t \]

      9. clear-num N/A

         \[\leadsto \frac{1}{z} \cdot \left(x \cdot \color{blue}{\frac{{y}^{3} - {a}^{3}}{y \cdot y + \left(a \cdot a + y \cdot a\right)}}\right) + t \]

      10. flip3-- N/A

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

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

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

      12. /-lowering-/.f64 N/A

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

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

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

      14. --lowering--.f64 99.6

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

   10. Applied egg-rr 99.6%

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

   11. Taylor expanded in t around inf

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

       1. +-commutative N/A

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

       2. distribute-lft-in N/A

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

       3. *-rgt-identity N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 100.0

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

   13. Simplified 100.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x \cdot \left(y - a\right)}{z \cdot t}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y - a, x - t, z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-219)
     t_1
     (if (<= t_2 2e-284) (/ (fma (- y a) (- x t) (* z t)) z) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -2e-219) {
		tmp = t_1;
	} else if (t_2 <= 2e-284) {
		tmp = fma((y - a), (x - t), (z * t)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-219)
		tmp = t_1;
	elseif (t_2 <= 2e-284)
		tmp = Float64(fma(Float64(y - a), Float64(x - t), Float64(z * t)) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-219], t$95$1, If[LessEqual[t$95$2, 2e-284], N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.0000000000000001e-219 or 2.00000000000000007e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 88.7

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

   4. Applied egg-rr 88.7%

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

   if -2.0000000000000001e-219 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000007e-284

   1. Initial program 6.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 96.6%

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

   6. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. --lowering--.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 99.8

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

   8. Simplified 99.8%

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

Alternative 3: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{z}, x \cdot \left(y - a\right), t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-219)
     t_1
     (if (<= t_2 2e-284) (fma (/ 1.0 z) (* x (- y a)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -2e-219) {
		tmp = t_1;
	} else if (t_2 <= 2e-284) {
		tmp = fma((1.0 / z), (x * (y - a)), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-219)
		tmp = t_1;
	elseif (t_2 <= 2e-284)
		tmp = fma(Float64(1.0 / z), Float64(x * Float64(y - a)), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-219], t$95$1, If[LessEqual[t$95$2, 2e-284], N[(N[(1.0 / z), $MachinePrecision] * N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.0000000000000001e-219 or 2.00000000000000007e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 88.7

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

   4. Applied egg-rr 88.7%

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

   if -2.0000000000000001e-219 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000007e-284

   1. Initial program 6.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 96.6%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 96.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-*l/ N/A

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

      4. div-inv N/A

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

      5. times-frac N/A

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

      6. flip3-- N/A

         \[\leadsto \frac{1}{z} \cdot \frac{x}{\frac{1}{\color{blue}{\frac{{y}^{3} - {a}^{3}}{y \cdot y + \left(a \cdot a + y \cdot a\right)}}}} + t \]

      7. clear-num N/A

         \[\leadsto \frac{1}{z} \cdot \frac{x}{\color{blue}{\frac{y \cdot y + \left(a \cdot a + y \cdot a\right)}{{y}^{3} - {a}^{3}}}} + t \]

      8. un-div-inv N/A

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{y \cdot y + \left(a \cdot a + y \cdot a\right)}{{y}^{3} - {a}^{3}}}\right)} + t \]

      9. clear-num N/A

         \[\leadsto \frac{1}{z} \cdot \left(x \cdot \color{blue}{\frac{{y}^{3} - {a}^{3}}{y \cdot y + \left(a \cdot a + y \cdot a\right)}}\right) + t \]

      10. flip3-- N/A

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

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

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

      12. /-lowering-/.f64 N/A

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

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

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

      14. --lowering--.f64 99.6

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

   10. Applied egg-rr 99.6%

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

Alternative 4: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y a) z) t)))
   (if (<= z -7.8e+19)
     t_1
     (if (<= z -3.3e-267)
       (* t (/ y (- a z)))
       (if (<= z 5.4e-99) x (if (<= z 3.2e+57) (* y (/ t (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((y - a) / z), t);
	double tmp;
	if (z <= -7.8e+19) {
		tmp = t_1;
	} else if (z <= -3.3e-267) {
		tmp = t * (y / (a - z));
	} else if (z <= 5.4e-99) {
		tmp = x;
	} else if (z <= 3.2e+57) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -7.8e+19)
		tmp = t_1;
	elseif (z <= -3.3e-267)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 5.4e-99)
		tmp = x;
	elseif (z <= 3.2e+57)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -7.8e+19], t$95$1, If[LessEqual[z, -3.3e-267], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-99], x, If[LessEqual[z, 3.2e+57], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8e19 or 3.20000000000000029e57 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 79.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 74.1%

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

   if -7.8e19 < z < -3.30000000000000004e-267

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 40.7

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

   5. Simplified 40.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 49.0

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

   7. Applied egg-rr 49.0%

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

   8. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 40.7

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

   10. Simplified 40.7%

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

   if -3.30000000000000004e-267 < z < 5.4e-99

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 48.1%

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

   if 5.4e-99 < z < 3.20000000000000029e57

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 66.9

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

   5. Simplified 66.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

      5. --lowering--.f64 54.5

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

   8. Simplified 54.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ y z) t)))
   (if (<= z -9.5e+33)
     t_1
     (if (<= z -1.05e-265)
       (* t (/ y (- a z)))
       (if (<= z 5e-100) x (if (<= z 5.2e+58) (* y (/ t (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (y / z), t);
	double tmp;
	if (z <= -9.5e+33) {
		tmp = t_1;
	} else if (z <= -1.05e-265) {
		tmp = t * (y / (a - z));
	} else if (z <= 5e-100) {
		tmp = x;
	} else if (z <= 5.2e+58) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(y / z), t)
	tmp = 0.0
	if (z <= -9.5e+33)
		tmp = t_1;
	elseif (z <= -1.05e-265)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 5e-100)
		tmp = x;
	elseif (z <= 5.2e+58)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -9.5e+33], t$95$1, If[LessEqual[z, -1.05e-265], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-100], x, If[LessEqual[z, 5.2e+58], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000003e33 or 5.19999999999999976e58 < z

   1. Initial program 45.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 75.9%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 69.4

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

   11. Simplified 69.4%

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

   if -9.5000000000000003e33 < z < -1.05000000000000002e-265

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 39.4

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

   5. Simplified 39.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 47.5

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

   7. Applied egg-rr 47.5%

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

   8. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 39.4

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

   10. Simplified 39.4%

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

   if -1.05000000000000002e-265 < z < 5.0000000000000001e-100

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 48.1%

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

   if 5.0000000000000001e-100 < z < 5.19999999999999976e58

   1. Initial program 82.5%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 64.9

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

   5. Simplified 64.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

      5. --lowering--.f64 52.9

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

   8. Simplified 52.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ t_2 := \mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))) (t_2 (fma x (/ y z) t)))
   (if (<= z -9e+33)
     t_2
     (if (<= z 1.08e-231)
       t_1
       (if (<= z 5.8e-98) x (if (<= z 5.2e+58) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double t_2 = fma(x, (y / z), t);
	double tmp;
	if (z <= -9e+33) {
		tmp = t_2;
	} else if (z <= 1.08e-231) {
		tmp = t_1;
	} else if (z <= 5.8e-98) {
		tmp = x;
	} else if (z <= 5.2e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	t_2 = fma(x, Float64(y / z), t)
	tmp = 0.0
	if (z <= -9e+33)
		tmp = t_2;
	elseif (z <= 1.08e-231)
		tmp = t_1;
	elseif (z <= 5.8e-98)
		tmp = x;
	elseif (z <= 5.2e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -9e+33], t$95$2, If[LessEqual[z, 1.08e-231], t$95$1, If[LessEqual[z, 5.8e-98], x, If[LessEqual[z, 5.2e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000001e33 or 5.19999999999999976e58 < z

   1. Initial program 45.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 75.9%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 69.4

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

   11. Simplified 69.4%

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

   if -9.0000000000000001e33 < z < 1.08e-231 or 5.8e-98 < z < 5.19999999999999976e58

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 47.4

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

   5. Simplified 47.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

      5. --lowering--.f64 43.2

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

   8. Simplified 43.2%

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

   if 1.08e-231 < z < 5.8e-98

   1. Initial program 91.6%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 58.5%

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

Alternative 7: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 72:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.4e+47)
     t
     (if (<= z -2.7e-279)
       t_1
       (if (<= z 2.1e-98) x (if (<= z 72.0) t_1 (fma a (/ t z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.4e+47) {
		tmp = t;
	} else if (z <= -2.7e-279) {
		tmp = t_1;
	} else if (z <= 2.1e-98) {
		tmp = x;
	} else if (z <= 72.0) {
		tmp = t_1;
	} else {
		tmp = fma(a, (t / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.4e+47)
		tmp = t;
	elseif (z <= -2.7e-279)
		tmp = t_1;
	elseif (z <= 2.1e-98)
		tmp = x;
	elseif (z <= 72.0)
		tmp = t_1;
	else
		tmp = fma(a, Float64(t / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+47], t, If[LessEqual[z, -2.7e-279], t$95$1, If[LessEqual[z, 2.1e-98], x, If[LessEqual[z, 72.0], t$95$1, N[(a * N[(t / z), $MachinePrecision] + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.39999999999999994e47

   1. Initial program 40.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 46.2%

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

   if -1.39999999999999994e47 < z < -2.7000000000000001e-279 or 2.09999999999999992e-98 < z < 72

   1. Initial program 86.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 46.2

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

   5. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 52.7

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

   7. Applied egg-rr 52.7%

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

   8. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 37.4

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

   10. Simplified 37.4%

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

   if -2.7000000000000001e-279 < z < 2.09999999999999992e-98

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 49.0%

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

   if 72 < z

   1. Initial program 54.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 49.3

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

   5. Simplified 49.3%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 45.6

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

   8. Simplified 45.6%

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

   9. Taylor expanded in z around inf

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

       1. sub-neg N/A

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

       2. associate-/l* N/A

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

       3. mul-1-neg N/A

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

       4. remove-double-neg N/A

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

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

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

       6. /-lowering-/.f64 49.9

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

   11. Simplified 49.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-279}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 72:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.4e+47)
     t
     (if (<= z -1.2e-275) t_1 (if (<= z 2.9e-96) x (if (<= z 6.0) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.4e+47) {
		tmp = t;
	} else if (z <= -1.2e-275) {
		tmp = t_1;
	} else if (z <= 2.9e-96) {
		tmp = x;
	} else if (z <= 6.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.4d+47)) then
        tmp = t
    else if (z <= (-1.2d-275)) then
        tmp = t_1
    else if (z <= 2.9d-96) then
        tmp = x
    else if (z <= 6.0d0) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.4e+47) {
		tmp = t;
	} else if (z <= -1.2e-275) {
		tmp = t_1;
	} else if (z <= 2.9e-96) {
		tmp = x;
	} else if (z <= 6.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.4e+47:
		tmp = t
	elif z <= -1.2e-275:
		tmp = t_1
	elif z <= 2.9e-96:
		tmp = x
	elif z <= 6.0:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.4e+47)
		tmp = t;
	elseif (z <= -1.2e-275)
		tmp = t_1;
	elseif (z <= 2.9e-96)
		tmp = x;
	elseif (z <= 6.0)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.4e+47)
		tmp = t;
	elseif (z <= -1.2e-275)
		tmp = t_1;
	elseif (z <= 2.9e-96)
		tmp = x;
	elseif (z <= 6.0)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+47], t, If[LessEqual[z, -1.2e-275], t$95$1, If[LessEqual[z, 2.9e-96], x, If[LessEqual[z, 6.0], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.39999999999999994e47 or 6 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 47.2%

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

   if -1.39999999999999994e47 < z < -1.19999999999999995e-275 or 2.89999999999999994e-96 < z < 6

   1. Initial program 86.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

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

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

      4. --lowering--.f64 46.2

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

   5. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 52.7

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

   7. Applied egg-rr 52.7%

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

   8. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 37.4

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

   10. Simplified 37.4%

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

   if -1.19999999999999995e-275 < z < 2.89999999999999994e-96

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 49.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ (- y a) z) t)))
   (if (<= z -5.5e+47)
     t_1
     (if (<= z 3.5e+59) (fma (- t x) (/ y (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((y - a) / z), t);
	double tmp;
	if (z <= -5.5e+47) {
		tmp = t_1;
	} else if (z <= 3.5e+59) {
		tmp = fma((t - x), (y / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -5.5e+47)
		tmp = t_1;
	elseif (z <= 3.5e+59)
		tmp = fma(Float64(t - x), Float64(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[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -5.5e+47], t$95$1, If[LessEqual[z, 3.5e+59], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999998e47 or 3.5e59 < z

   1. Initial program 44.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 81.4%

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

   if -5.4999999999999998e47 < z < 3.5e59

   1. Initial program 88.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 93.3

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 85.2

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

   7. Simplified 85.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x t) z) (- y a) t)))
   (if (<= z -1.1e+78)
     t_1
     (if (<= z 7e+59) (fma (- t x) (/ y (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - t) / z), (y - a), t);
	double tmp;
	if (z <= -1.1e+78) {
		tmp = t_1;
	} else if (z <= 7e+59) {
		tmp = fma((t - x), (y / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - t) / z), Float64(y - a), t)
	tmp = 0.0
	if (z <= -1.1e+78)
		tmp = t_1;
	elseif (z <= 7e+59)
		tmp = fma(Float64(t - x), Float64(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[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -1.1e+78], t$95$1, If[LessEqual[z, 7e+59], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000007e78 or 7e59 < z

   1. Initial program 42.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 82.9%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. unsub-neg N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 81.8

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

   7. Applied egg-rr 81.8%

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

   if -1.10000000000000007e78 < z < 7e59

   1. Initial program 87.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 92.2

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 83.7

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

   7. Simplified 83.7%

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

Alternative 11: 78.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y - a, t\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+79)
   (fma (/ x z) (- y a) t)
   (if (<= z 3.1e+59) (fma (- t x) (/ y (- a z)) x) (fma (- x t) (/ y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+79) {
		tmp = fma((x / z), (y - a), t);
	} else if (z <= 3.1e+59) {
		tmp = fma((t - x), (y / (a - z)), x);
	} else {
		tmp = fma((x - t), (y / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+79)
		tmp = fma(Float64(x / z), Float64(y - a), t);
	elseif (z <= 3.1e+59)
		tmp = fma(Float64(t - x), Float64(y / Float64(a - z)), x);
	else
		tmp = fma(Float64(x - t), Float64(y / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+79], N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 3.1e+59], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999993e79

   1. Initial program 35.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 80.4%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 82.4

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

   10. Applied egg-rr 82.4%

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

   if -1.19999999999999993e79 < z < 3.10000000000000015e59

   1. Initial program 87.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 N/A

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

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

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

      8. --lowering--.f64 92.2

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 83.7

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

   7. Simplified 83.7%

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

   if 3.10000000000000015e59 < z

   1. Initial program 48.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 81.9%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 77.9

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

   8. Simplified 77.9%

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

Alternative 12: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y - a, t\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+34)
   (fma (/ x z) (- y a) t)
   (if (<= z 1.5e-27) (fma y (/ (- t x) a) x) (fma (- x t) (/ y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+34) {
		tmp = fma((x / z), (y - a), t);
	} else if (z <= 1.5e-27) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = fma((x - t), (y / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+34)
		tmp = fma(Float64(x / z), Float64(y - a), t);
	elseif (z <= 1.5e-27)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(x - t), Float64(y / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+34], N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 1.5e-27], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000001e34

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 80.7%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 75.9%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

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

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

      11. --lowering--.f64 76.0

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

   10. Applied egg-rr 76.0%

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

   if -3.8000000000000001e34 < z < 1.5000000000000001e-27

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 76.4

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

   5. Simplified 76.4%

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

   if 1.5000000000000001e-27 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 77.7%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 73.3

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

   8. Simplified 73.3%

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

Alternative 13: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+34)
   (fma x (/ (- y a) z) t)
   (if (<= z 2.2e-29) (fma y (/ (- t x) a) x) (fma (- x t) (/ y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+34) {
		tmp = fma(x, ((y - a) / z), t);
	} else if (z <= 2.2e-29) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = fma((x - t), (y / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+34)
		tmp = fma(x, Float64(Float64(y - a) / z), t);
	elseif (z <= 2.2e-29)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(x - t), Float64(y / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+34], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 2.2e-29], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999995e34

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 80.7%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 75.9%

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

   if -5.19999999999999995e34 < z < 2.1999999999999999e-29

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 76.4

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

   5. Simplified 76.4%

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

   if 2.1999999999999999e-29 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 77.7%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 73.3

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

   8. Simplified 73.3%

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

Alternative 14: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y a) z) t)))
   (if (<= z -2.5e+34) t_1 (if (<= z 2.05e+82) (fma y (/ (- t x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((y - a) / z), t);
	double tmp;
	if (z <= -2.5e+34) {
		tmp = t_1;
	} else if (z <= 2.05e+82) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -2.5e+34)
		tmp = t_1;
	elseif (z <= 2.05e+82)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -2.5e+34], t$95$1, If[LessEqual[z, 2.05e+82], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e34 or 2.04999999999999998e82 < z

   1. Initial program 44.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 81.9%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 77.1%

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

   if -2.4999999999999999e34 < z < 2.04999999999999998e82

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 71.3

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

   5. Simplified 71.3%

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

Alternative 15: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+174) x (if (<= a 1.9e+65) (fma x (/ y z) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+174) {
		tmp = x;
	} else if (a <= 1.9e+65) {
		tmp = fma(x, (y / z), t);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+174)
		tmp = x;
	elseif (a <= 1.9e+65)
		tmp = fma(x, Float64(y / z), t);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+174], x, If[LessEqual[a, 1.9e+65], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000001e174 or 1.90000000000000006e65 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 49.5%

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

   if -6.5000000000000001e174 < a < 1.90000000000000006e65

   1. Initial program 66.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 56.8%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 53.8

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

   11. Simplified 53.8%

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

Alternative 16: 38.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+80)
   t
   (if (<= z -1.85e+34) (* x (/ y z)) (if (<= z 2.05e+59) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+80) {
		tmp = t;
	} else if (z <= -1.85e+34) {
		tmp = x * (y / z);
	} else if (z <= 2.05e+59) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+80)) then
        tmp = t
    else if (z <= (-1.85d+34)) then
        tmp = x * (y / z)
    else if (z <= 2.05d+59) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+80) {
		tmp = t;
	} else if (z <= -1.85e+34) {
		tmp = x * (y / z);
	} else if (z <= 2.05e+59) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+80:
		tmp = t
	elif z <= -1.85e+34:
		tmp = x * (y / z)
	elif z <= 2.05e+59:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+80)
		tmp = t;
	elseif (z <= -1.85e+34)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 2.05e+59)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+80)
		tmp = t;
	elseif (z <= -1.85e+34)
		tmp = x * (y / z);
	elseif (z <= 2.05e+59)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+80], t, If[LessEqual[z, -1.85e+34], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+59], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999991e80 or 2.05e59 < z

   1. Initial program 41.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 55.0%

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

   if -3.29999999999999991e80 < z < -1.85000000000000004e34

   1. Initial program 76.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

   5. Simplified 69.9%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 62.1%

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

   9. Taylor expanded in y around inf

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

       1. associate-/l* N/A

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

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

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

       3. /-lowering-/.f64 47.6

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

   11. Simplified 47.6%

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

   if -1.85000000000000004e34 < z < 2.05e59

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 31.3%

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

Alternative 17: 38.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+90) x (if (<= a 3.7e+69) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+90) {
		tmp = x;
	} else if (a <= 3.7e+69) {
		tmp = t;
	} else {
		tmp = 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 (a <= (-2.05d+90)) then
        tmp = x
    else if (a <= 3.7d+69) then
        tmp = t
    else
        tmp = 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 (a <= -2.05e+90) {
		tmp = x;
	} else if (a <= 3.7e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+90:
		tmp = x
	elif a <= 3.7e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+90)
		tmp = x;
	elseif (a <= 3.7e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+90)
		tmp = x;
	elseif (a <= 3.7e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+90], x, If[LessEqual[a, 3.7e+69], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05000000000000021e90 or 3.6999999999999999e69 < a

   1. Initial program 78.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.5%

      \[\leadsto \color{blue}{x} \]

   if -2.05000000000000021e90 < a < 3.6999999999999999e69

   1. Initial program 66.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 35.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 25.1% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 69.9%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 26.0%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - 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 a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))