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

Percentage Accurate: 67.6% → 88.8%

Time: 10.3s

Alternatives: 20

Speedup: 0.8×

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: 67.6% 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: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+208} \lor \neg \left(z \leq 7 \cdot 10^{+147}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+208) (not (<= z 7e+147)))
   (- t (* (/ (- t x) z) (- y a)))
   (fma (- t x) (/ (- y z) (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+208) || !(z <= 7e+147)) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+208) || !(z <= 7e+147))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+208], N[Not[LessEqual[z, 7e+147]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85000000000000015e208 or 6.99999999999999949e147 < z

   1. Initial program 19.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 56.1

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 93.2

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

   7. Applied rewrites 93.2%

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

   if -2.85000000000000015e208 < z < 6.99999999999999949e147

   1. Initial program 76.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.8

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

   4. Applied rewrites 90.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+208} \lor \neg \left(z \leq 7 \cdot 10^{+147}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ t_2 := \mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -880000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-194}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* (- t x) (- y a)) z)))
        (t_2 (fma (/ (- y z) a) (- t x) x)))
   (if (<= a -880000000000.0)
     t_2
     (if (<= a -4.2e-80)
       t_1
       (if (<= a -3.7e-194)
         (* (- t x) (/ y (- a z)))
         (if (<= a 2.65e-36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) * (y - a)) / z);
	double t_2 = fma(((y - z) / a), (t - x), x);
	double tmp;
	if (a <= -880000000000.0) {
		tmp = t_2;
	} else if (a <= -4.2e-80) {
		tmp = t_1;
	} else if (a <= -3.7e-194) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.65e-36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z))
	t_2 = fma(Float64(Float64(y - z) / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -880000000000.0)
		tmp = t_2;
	elseif (a <= -4.2e-80)
		tmp = t_1;
	elseif (a <= -3.7e-194)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 2.65e-36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -880000000000.0], t$95$2, If[LessEqual[a, -4.2e-80], t$95$1, If[LessEqual[a, -3.7e-194], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.8e11 or 2.6499999999999999e-36 < a

   1. Initial program 69.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.6

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

   4. Applied rewrites 92.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 77.8

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

   7. Applied rewrites 77.8%

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

   if -8.8e11 < a < -4.20000000000000003e-80 or -3.70000000000000008e-194 < a < 2.6499999999999999e-36

   1. Initial program 56.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 43.0

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

   7. Applied rewrites 43.0%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 50.4

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

   10. Applied rewrites 50.4%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   12. 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. associate-*r/ N/A

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

       3. associate-*r/ N/A

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

       4. mul-1-neg N/A

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

       5. div-sub N/A

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

       6. mul-1-neg N/A

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

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

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

       8. associate-*r/ N/A

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

       9. mul-1-neg N/A

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

       10. unsub-neg N/A

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

       11. lower--.f64 N/A

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

       12. lower-/.f64 N/A

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

   13. Applied rewrites 84.3%

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

   if -4.20000000000000003e-80 < a < -3.70000000000000008e-194

   1. Initial program 83.1%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -880000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-194}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-117}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t) (/ z (- a z)))))
   (if (<= z -1.55e+105)
     t_1
     (if (<= z 3.5e-117)
       (fma (/ y a) (- t x) x)
       (if (<= z 4.5e+106) (* (- t x) (/ y (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (z / (a - z));
	double tmp;
	if (z <= -1.55e+105) {
		tmp = t_1;
	} else if (z <= 3.5e-117) {
		tmp = fma((y / a), (t - x), x);
	} else if (z <= 4.5e+106) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) * Float64(z / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.55e+105)
		tmp = t_1;
	elseif (z <= 3.5e-117)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	elseif (z <= 4.5e+106)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+105], t$95$1, If[LessEqual[z, 3.5e-117], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4.5e+106], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000002e105 or 4.4999999999999997e106 < z

   1. Initial program 30.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 66.1

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

   4. Applied rewrites 66.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 57.5

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

   7. Applied rewrites 57.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 58.3%

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

   if -1.55000000000000002e105 < z < 3.4999999999999998e-117

   1. Initial program 85.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 93.8

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 75.8

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

   7. Applied rewrites 75.8%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 71.1%

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

   if 3.4999999999999998e-117 < z < 4.4999999999999997e106

   1. Initial program 70.4%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 65.1

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

   5. Applied rewrites 65.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+105}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-117}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -64000000000000 \lor \neg \left(a \leq 3.9 \cdot 10^{-10}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -64000000000000.0) (not (<= a 3.9e-10)))
   (fma (/ (- y z) a) (- t x) x)
   (- t (* (/ (- t x) z) (- y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -64000000000000.0) || !(a <= 3.9e-10)) {
		tmp = fma(((y - z) / a), (t - x), x);
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -64000000000000.0) || !(a <= 3.9e-10))
		tmp = fma(Float64(Float64(y - z) / a), Float64(t - x), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -64000000000000.0], N[Not[LessEqual[a, 3.9e-10]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4e13 or 3.9e-10 < a

   1. Initial program 69.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 79.2

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

   7. Applied rewrites 79.2%

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

   if -6.4e13 < a < 3.9e-10

   1. Initial program 61.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 74.8

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

   4. Applied rewrites 74.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 79.7

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

   7. Applied rewrites 79.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -64000000000000 \lor \neg \left(a \leq 3.9 \cdot 10^{-10}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;\frac{t}{a - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t x))))
   (if (<= z -8e+98)
     t_1
     (if (<= z 4.6e-157)
       (* (/ (- t x) a) y)
       (if (<= z 2.8e+209) (* (/ t (- a z)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -8e+98) {
		tmp = t_1;
	} else if (z <= 4.6e-157) {
		tmp = ((t - x) / a) * y;
	} else if (z <= 2.8e+209) {
		tmp = (t / (a - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t - x)
    if (z <= (-8d+98)) then
        tmp = t_1
    else if (z <= 4.6d-157) then
        tmp = ((t - x) / a) * y
    else if (z <= 2.8d+209) then
        tmp = (t / (a - z)) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -8e+98) {
		tmp = t_1;
	} else if (z <= 4.6e-157) {
		tmp = ((t - x) / a) * y;
	} else if (z <= 2.8e+209) {
		tmp = (t / (a - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -8e+98:
		tmp = t_1
	elif z <= 4.6e-157:
		tmp = ((t - x) / a) * y
	elif z <= 2.8e+209:
		tmp = (t / (a - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -8e+98)
		tmp = t_1;
	elseif (z <= 4.6e-157)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	elseif (z <= 2.8e+209)
		tmp = Float64(Float64(t / Float64(a - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - x);
	tmp = 0.0;
	if (z <= -8e+98)
		tmp = t_1;
	elseif (z <= 4.6e-157)
		tmp = ((t - x) / a) * y;
	elseif (z <= 2.8e+209)
		tmp = (t / (a - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+98], t$95$1, If[LessEqual[z, 4.6e-157], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 2.8e+209], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999998e98 or 2.80000000000000013e209 < z

   1. Initial program 32.0%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 43.6

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

   5. Applied rewrites 43.6%

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

   if -7.99999999999999998e98 < z < 4.59999999999999977e-157

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.2

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

   4. Applied rewrites 94.2%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 76.4

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

   7. Applied rewrites 76.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 40.3%

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

   if 4.59999999999999977e-157 < z < 2.80000000000000013e209

   1. Initial program 59.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 55.0

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

   7. Applied rewrites 55.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 39.7%

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

   12. Applied rewrites 39.8%

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

Alternative 6: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+55} \lor \neg \left(z \leq 3.5 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e+55) (not (<= z 3.5e-117)))
   (* t (/ (- y z) (- a z)))
   (fma (/ (- y z) a) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+55) || !(z <= 3.5e-117)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = fma(((y - z) / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e+55) || !(z <= 3.5e-117))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = fma(Float64(Float64(y - z) / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e+55], N[Not[LessEqual[z, 3.5e-117]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999999e55 or 3.4999999999999998e-117 < z

   1. Initial program 45.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 74.8

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

   4. Applied rewrites 74.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   9. Applied rewrites 66.3%

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

   if -2.24999999999999999e55 < z < 3.4999999999999998e-117

   1. Initial program 86.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.0

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

   4. Applied rewrites 94.0%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 78.0

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

   7. Applied rewrites 78.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+55} \lor \neg \left(z \leq 3.5 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+16} \lor \neg \left(a \leq 2 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e+16) (not (<= a 2e-44)))
   (fma (- y z) (/ (- t x) a) x)
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e+16) || !(a <= 2e-44)) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.4e+16) || !(a <= 2e-44))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.4e+16], N[Not[LessEqual[a, 2e-44]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4e16 or 1.99999999999999991e-44 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -2.4e16 < a < 1.99999999999999991e-44

   1. Initial program 61.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 74.1

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

   4. Applied rewrites 74.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   9. Applied rewrites 63.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+16} \lor \neg \left(a \leq 2 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+55} \lor \neg \left(z \leq 3.2 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+55) (not (<= z 3.2e-117)))
   (* t (/ (- y z) (- a z)))
   (fma (/ y a) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+55) || !(z <= 3.2e-117)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+55) || !(z <= 3.2e-117))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+55], N[Not[LessEqual[z, 3.2e-117]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000005e55 or 3.19999999999999995e-117 < z

   1. Initial program 45.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 74.8

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

   4. Applied rewrites 74.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   9. Applied rewrites 66.3%

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

   if -1.75000000000000005e55 < z < 3.19999999999999995e-117

   1. Initial program 86.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.0

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

   4. Applied rewrites 94.0%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 78.0

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

   7. Applied rewrites 78.0%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 74.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+55} \lor \neg \left(z \leq 3.2 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+55} \lor \neg \left(z \leq 2.9 \cdot 10^{-116}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+55) (not (<= z 2.9e-116)))
   (* (- y z) (/ t (- a z)))
   (fma (/ y a) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+55) || !(z <= 2.9e-116)) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+55) || !(z <= 2.9e-116))
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+55], N[Not[LessEqual[z, 2.9e-116]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000014e55 or 2.8999999999999998e-116 < z

   1. Initial program 45.4%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if -1.95000000000000014e55 < z < 2.8999999999999998e-116

   1. Initial program 86.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 74.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+55} \lor \neg \left(z \leq 2.9 \cdot 10^{-116}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 24.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+74}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y x) z)))
   (if (<= x -5.1e-96)
     t_1
     (if (<= x -1.9e-231)
       (/ (* y t) a)
       (if (<= x 6.5e+74) (+ x (- t x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) / z;
	double tmp;
	if (x <= -5.1e-96) {
		tmp = t_1;
	} else if (x <= -1.9e-231) {
		tmp = (y * t) / a;
	} else if (x <= 6.5e+74) {
		tmp = x + (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 = (y * x) / z
    if (x <= (-5.1d-96)) then
        tmp = t_1
    else if (x <= (-1.9d-231)) then
        tmp = (y * t) / a
    else if (x <= 6.5d+74) then
        tmp = x + (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 = (y * x) / z;
	double tmp;
	if (x <= -5.1e-96) {
		tmp = t_1;
	} else if (x <= -1.9e-231) {
		tmp = (y * t) / a;
	} else if (x <= 6.5e+74) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * x) / z
	tmp = 0
	if x <= -5.1e-96:
		tmp = t_1
	elif x <= -1.9e-231:
		tmp = (y * t) / a
	elif x <= 6.5e+74:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * x) / z)
	tmp = 0.0
	if (x <= -5.1e-96)
		tmp = t_1;
	elseif (x <= -1.9e-231)
		tmp = Float64(Float64(y * t) / a);
	elseif (x <= 6.5e+74)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * x) / z;
	tmp = 0.0;
	if (x <= -5.1e-96)
		tmp = t_1;
	elseif (x <= -1.9e-231)
		tmp = (y * t) / a;
	elseif (x <= 6.5e+74)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -5.1e-96], t$95$1, If[LessEqual[x, -1.9e-231], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 6.5e+74], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.09999999999999973e-96 or 6.49999999999999962e74 < x

   1. Initial program 57.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 76.3

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

   4. Applied rewrites 76.3%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 46.1

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

   7. Applied rewrites 46.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 33.4%

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

   11. Taylor expanded in x around inf

       \[\leadsto \frac{x \cdot y}{z} \]
   12. Step-by-step derivation

   13. Applied rewrites 25.4%

       \[\leadsto \frac{y \cdot x}{z} \]

   if -5.09999999999999973e-96 < x < -1.90000000000000007e-231

   1. Initial program 75.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 61.4

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

   7. Applied rewrites 61.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 50.7%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 36.1%

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

   if -1.90000000000000007e-231 < x < 6.49999999999999962e74

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 30.3

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

   5. Applied rewrites 30.3%

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

Alternative 11: 63.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+105} \lor \neg \left(z \leq 8.5 \cdot 10^{+105}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+105) (not (<= z 8.5e+105)))
   (* (- t) (/ z (- a z)))
   (fma (/ y a) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+105) || !(z <= 8.5e+105)) {
		tmp = -t * (z / (a - z));
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+105) || !(z <= 8.5e+105))
		tmp = Float64(Float64(-t) * Float64(z / Float64(a - z)));
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+105], N[Not[LessEqual[z, 8.5e+105]], $MachinePrecision]], N[((-t) * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000002e105 or 8.49999999999999986e105 < z

   1. Initial program 30.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 66.1

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

   4. Applied rewrites 66.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 57.5

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

   7. Applied rewrites 57.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 58.3%

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

   if -1.55000000000000002e105 < z < 8.49999999999999986e105

   1. Initial program 82.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.8

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

   4. Applied rewrites 92.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 71.7

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 66.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+105} \lor \neg \left(z \leq 8.5 \cdot 10^{+105}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-194} \lor \neg \left(a \leq 1.55 \cdot 10^{-52}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.7e-194) (not (<= a 1.55e-52)))
   (fma (/ y a) (- t x) x)
   (* (- y) (/ (- t x) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e-194) || !(a <= 1.55e-52)) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = -y * ((t - x) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.7e-194) || !(a <= 1.55e-52))
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = Float64(Float64(-y) * Float64(Float64(t - x) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.7e-194], N[Not[LessEqual[a, 1.55e-52]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[((-y) * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.70000000000000008e-194 or 1.5499999999999999e-52 < a

   1. Initial program 69.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.8

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 71.8

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

   7. Applied rewrites 71.8%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 64.3%

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

   if -3.70000000000000008e-194 < a < 1.5499999999999999e-52

   1. Initial program 56.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 69.5

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

   4. Applied rewrites 69.5%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 48.1

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

   7. Applied rewrites 48.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 46.0%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-194} \lor \neg \left(a \leq 1.55 \cdot 10^{-52}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+105} \lor \neg \left(z \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+105) (not (<= z 7.2e+113)))
   (+ x (- t x))
   (fma (/ y a) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+105) || !(z <= 7.2e+113)) {
		tmp = x + (t - x);
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+105) || !(z <= 7.2e+113))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+105], N[Not[LessEqual[z, 7.2e+113]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999992e105 or 7.19999999999999984e113 < z

   1. Initial program 28.6%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 37.9

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

   5. Applied rewrites 37.9%

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

   if -1.84999999999999992e105 < z < 7.19999999999999984e113

   1. Initial program 82.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 71.6

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

   7. Applied rewrites 71.6%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 65.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+105} \lor \neg \left(z \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+105} \lor \neg \left(z \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+105) (not (<= z 7.2e+113)))
   (+ x (- t x))
   (fma (/ (- t x) a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+105) || !(z <= 7.2e+113)) {
		tmp = x + (t - x);
	} else {
		tmp = fma(((t - x) / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+105) || !(z <= 7.2e+113))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+105], N[Not[LessEqual[z, 7.2e+113]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999992e105 or 7.19999999999999984e113 < z

   1. Initial program 28.6%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 37.9

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

   5. Applied rewrites 37.9%

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

   if -1.84999999999999992e105 < z < 7.19999999999999984e113

   1. Initial program 82.3%

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 64.0

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

   5. Applied rewrites 64.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+105} \lor \neg \left(z \leq 7.2 \cdot 10^{+113}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72} \lor \neg \left(y \leq 1.2 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.1e+72) (not (<= y 1.2e+64)))
   (* (/ (- t x) a) y)
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e+72) || !(y <= 1.2e+64)) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = x + ((y * t) / a);
	}
	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 ((y <= (-1.1d+72)) .or. (.not. (y <= 1.2d+64))) then
        tmp = ((t - x) / a) * y
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e+72) || !(y <= 1.2e+64)) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.1e+72) or not (y <= 1.2e+64):
		tmp = ((t - x) / a) * y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.1e+72) || !(y <= 1.2e+64))
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.1e+72) || ~((y <= 1.2e+64)))
		tmp = ((t - x) / a) * y;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.1e+72], N[Not[LessEqual[y, 1.2e+64]], $MachinePrecision]], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e72 or 1.2e64 < y

   1. Initial program 62.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.6

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 56.3

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

   7. Applied rewrites 56.3%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 49.4%

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

   if -1.1e72 < y < 1.2e64

   1. Initial program 66.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 42.9

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

   5. Applied rewrites 42.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.0%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72} \lor \neg \left(y \leq 1.2 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+95} \lor \neg \left(z \leq 2.8 \cdot 10^{+209}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+95) (not (<= z 2.8e+209)))
   (+ x (- t x))
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+95) || !(z <= 2.8e+209)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / (a - z));
	}
	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 <= (-4.3d+95)) .or. (.not. (z <= 2.8d+209))) then
        tmp = x + (t - x)
    else
        tmp = t * (y / (a - z))
    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 <= -4.3e+95) || !(z <= 2.8e+209)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e+95) or not (z <= 2.8e+209):
		tmp = x + (t - x)
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e+95) || !(z <= 2.8e+209))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e+95) || ~((z <= 2.8e+209)))
		tmp = x + (t - x);
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e+95], N[Not[LessEqual[z, 2.8e+209]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3e95 or 2.80000000000000013e209 < z

   1. Initial program 33.9%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 43.8

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

   5. Applied rewrites 43.8%

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

   if -4.3e95 < z < 2.80000000000000013e209

   1. Initial program 76.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.7

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

   4. Applied rewrites 89.7%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 53.6

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

   7. Applied rewrites 53.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 32.1%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+95} \lor \neg \left(z \leq 2.8 \cdot 10^{+209}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-41} \lor \neg \left(z \leq 3.9 \cdot 10^{+159}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e-41) (not (<= z 3.9e+159))) (+ x (- t x)) (/ (* y t) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e-41) || !(z <= 3.9e+159)) {
		tmp = x + (t - x);
	} else {
		tmp = (y * t) / a;
	}
	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 <= (-5.5d-41)) .or. (.not. (z <= 3.9d+159))) then
        tmp = x + (t - x)
    else
        tmp = (y * t) / a
    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 <= -5.5e-41) || !(z <= 3.9e+159)) {
		tmp = x + (t - x);
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e-41) or not (z <= 3.9e+159):
		tmp = x + (t - x)
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e-41) || !(z <= 3.9e+159))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e-41) || ~((z <= 3.9e+159)))
		tmp = x + (t - x);
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e-41], N[Not[LessEqual[z, 3.9e+159]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000022e-41 or 3.9000000000000001e159 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 34.8

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

   5. Applied rewrites 34.8%

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

   if -5.50000000000000022e-41 < z < 3.9000000000000001e159

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 55.7

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

   7. Applied rewrites 55.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 33.8%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 20.5%

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

4. Final simplification 26.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-41} \lor \neg \left(z \leq 3.9 \cdot 10^{+159}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-9}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e-9)
   (+ x (- t x))
   (if (<= t 5.5e-67) (/ (* y x) z) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-9) {
		tmp = x + (t - x);
	} else if (t <= 5.5e-67) {
		tmp = (y * x) / z;
	} else {
		tmp = t * (y / a);
	}
	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 (t <= (-2.2d-9)) then
        tmp = x + (t - x)
    else if (t <= 5.5d-67) then
        tmp = (y * x) / z
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-9) {
		tmp = x + (t - x);
	} else if (t <= 5.5e-67) {
		tmp = (y * x) / z;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e-9:
		tmp = x + (t - x)
	elif t <= 5.5e-67:
		tmp = (y * x) / z
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e-9)
		tmp = Float64(x + Float64(t - x));
	elseif (t <= 5.5e-67)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e-9)
		tmp = x + (t - x);
	elseif (t <= 5.5e-67)
		tmp = (y * x) / z;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e-9], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-67], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999998e-9

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 30.2

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

   5. Applied rewrites 30.2%

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

   if -2.1999999999999998e-9 < t < 5.5000000000000003e-67

   1. Initial program 67.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 72.7

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

   4. Applied rewrites 72.7%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 51.3

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 33.7%

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

   11. Taylor expanded in x around inf

       \[\leadsto \frac{x \cdot y}{z} \]
   12. Step-by-step derivation

   13. Applied rewrites 27.6%

       \[\leadsto \frac{y \cdot x}{z} \]

   if 5.5000000000000003e-67 < t

   1. Initial program 68.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.6

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 50.8

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

   7. Applied rewrites 50.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 40.6%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 34.9%

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

Alternative 19: 19.8% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.1%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 19.3

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

5. Applied rewrites 19.3%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
6. Add Preprocessing

Alternative 20: 2.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ x + \left(-x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.1%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 19.3

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

5. Applied rewrites 19.3%

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

6. Taylor expanded in x around inf

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
7. Step-by-step derivation

8. Applied rewrites 2.8%

   \[\leadsto x + \left(-x\right) \]
9. Add Preprocessing

Developer Target 1: 84.3% 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 2024313 
(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))))