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

Percentage Accurate: 68.1% → 86.6%

Time: 8.8s

Alternatives: 13

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), t\_1, t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y, t\_1, \left(\left(-\left(t - x\right)\right) \cdot \frac{y - a}{z}\right) \cdot \frac{a}{z}\right) + t\right) + a \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) z)))
   (if (<= z -1.7e+177)
     (fma (fma -1.0 y a) t_1 t)
     (if (<= z 6.2e+160)
       (fma (/ (- t x) (- a z)) (- y z) x)
       (+
        (+ (fma (- y) t_1 (* (* (- (- t x)) (/ (- y a) z)) (/ a z))) t)
        (* a t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / z;
	double tmp;
	if (z <= -1.7e+177) {
		tmp = fma(fma(-1.0, y, a), t_1, t);
	} else if (z <= 6.2e+160) {
		tmp = fma(((t - x) / (a - z)), (y - z), x);
	} else {
		tmp = (fma(-y, t_1, ((-(t - x) * ((y - a) / z)) * (a / z))) + t) + (a * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / z)
	tmp = 0.0
	if (z <= -1.7e+177)
		tmp = fma(fma(-1.0, y, a), t_1, t);
	elseif (z <= 6.2e+160)
		tmp = fma(Float64(Float64(t - x) / Float64(a - z)), Float64(y - z), x);
	else
		tmp = Float64(Float64(fma(Float64(-y), t_1, Float64(Float64(Float64(-Float64(t - x)) * Float64(Float64(y - a) / z)) * Float64(a / z))) + t) + Float64(a * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.7e+177], N[(N[(-1.0 * y + a), $MachinePrecision] * t$95$1 + t), $MachinePrecision], If[LessEqual[z, 6.2e+160], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[((-y) * t$95$1 + N[(N[((-N[(t - x), $MachinePrecision]) * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6999999999999999e177

   1. Initial program 21.2%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 48.8

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

   4. Applied rewrites 48.8%

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

   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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

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

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

      10. associate-*r/ N/A

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

   7. Applied rewrites 94.3%

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

   if -1.6999999999999999e177 < z < 6.1999999999999996e160

   1. Initial program 80.3%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 88.5

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

   4. Applied rewrites 88.5%

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

   if 6.1999999999999996e160 < z

   1. Initial program 30.9%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 50.1

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

   4. Applied rewrites 50.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. difference-of-squares N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 9.9

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

   6. Applied rewrites 9.9%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 89.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), \frac{t - x}{z}, t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y, \frac{t - x}{z}, \left(\left(-\left(t - x\right)\right) \cdot \frac{y - a}{z}\right) \cdot \frac{a}{z}\right) + t\right) + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+177} \lor \neg \left(z \leq 6.2 \cdot 10^{+160}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+177) (not (<= z 6.2e+160)))
   (fma (fma -1.0 y a) (/ (- t x) z) t)
   (fma (/ (- t x) (- a z)) (- y z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+177) || !(z <= 6.2e+160)) {
		tmp = fma(fma(-1.0, y, a), ((t - x) / z), t);
	} else {
		tmp = fma(((t - x) / (a - z)), (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+177) || !(z <= 6.2e+160))
		tmp = fma(fma(-1.0, y, a), Float64(Float64(t - x) / z), t);
	else
		tmp = fma(Float64(Float64(t - x) / Float64(a - z)), Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+177], N[Not[LessEqual[z, 6.2e+160]], $MachinePrecision]], N[(N[(-1.0 * y + a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e177 or 6.1999999999999996e160 < z

   1. Initial program 25.5%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 49.4

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

   4. Applied rewrites 49.4%

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

   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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

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

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

      10. associate-*r/ N/A

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

   7. Applied rewrites 91.6%

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

   if -1.6999999999999999e177 < z < 6.1999999999999996e160

   1. Initial program 80.3%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 88.5

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

   4. Applied rewrites 88.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+177} \lor \neg \left(z \leq 6.2 \cdot 10^{+160}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-51} \lor \neg \left(z \leq 6.4 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e-51) (not (<= z 6.4e+17)))
   (fma (fma -1.0 y a) (/ (- t x) z) t)
   (fma (- y z) (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-51) || !(z <= 6.4e+17)) {
		tmp = fma(fma(-1.0, y, a), ((t - x) / z), t);
	} else {
		tmp = fma((y - z), ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e-51) || !(z <= 6.4e+17))
		tmp = fma(fma(-1.0, y, a), Float64(Float64(t - x) / z), t);
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e-51], N[Not[LessEqual[z, 6.4e+17]], $MachinePrecision]], N[(N[(-1.0 * y + a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999997e-51 or 6.4e17 < z

   1. Initial program 45.3%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 66.9

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

   4. Applied rewrites 66.9%

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

   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

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

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

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

      10. associate-*r/ N/A

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

   7. Applied rewrites 78.2%

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

   if -3.4999999999999997e-51 < z < 6.4e17

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-51} \lor \neg \left(z \leq 6.4 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, y, a\right), \frac{t - x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y a) z) t)))
   (if (<= z -3.6e-51)
     t_1
     (if (<= z 8e+17)
       (fma (- y z) (/ (- t x) a) x)
       (if (<= z 1.25e+196) (fma (/ (- x t) z) y t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((y - a) / z), t);
	double tmp;
	if (z <= -3.6e-51) {
		tmp = t_1;
	} else if (z <= 8e+17) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else if (z <= 1.25e+196) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -3.6e-51)
		tmp = t_1;
	elseif (z <= 8e+17)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	elseif (z <= 1.25e+196)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -3.6e-51], t$95$1, If[LessEqual[z, 8e+17], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.25e+196], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-51 or 1.2499999999999999e196 < z

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.2%

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

   if -3.6e-51 < z < 8e17

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   if 8e17 < z < 1.2499999999999999e196

   1. Initial program 56.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. div-sub N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.7

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

   8. Applied rewrites 63.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y a) z) t)))
   (if (<= z -3.6e-51)
     t_1
     (if (<= z 2.3e+16)
       (fma (/ (- t x) a) y x)
       (if (<= z 1.25e+196) (fma (/ (- x t) z) y t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((y - a) / z), t);
	double tmp;
	if (z <= -3.6e-51) {
		tmp = t_1;
	} else if (z <= 2.3e+16) {
		tmp = fma(((t - x) / a), y, x);
	} else if (z <= 1.25e+196) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -3.6e-51)
		tmp = t_1;
	elseif (z <= 2.3e+16)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	elseif (z <= 1.25e+196)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -3.6e-51], t$95$1, If[LessEqual[z, 2.3e+16], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 1.25e+196], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-51 or 1.2499999999999999e196 < z

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.2%

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

   if -3.6e-51 < z < 2.3e16

   1. Initial program 91.8%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if 2.3e16 < z < 1.2499999999999999e196

   1. Initial program 56.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. div-sub N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.7

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

   8. Applied rewrites 63.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y a) z) t)))
   (if (<= z -3e-51)
     t_1
     (if (<= z 2.3e+16)
       (fma y (/ t a) x)
       (if (<= z 1.25e+196) (fma (/ (- x t) z) y t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, ((y - a) / z), t);
	double tmp;
	if (z <= -3e-51) {
		tmp = t_1;
	} else if (z <= 2.3e+16) {
		tmp = fma(y, (t / a), x);
	} else if (z <= 1.25e+196) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -3e-51)
		tmp = t_1;
	elseif (z <= 2.3e+16)
		tmp = fma(y, Float64(t / a), x);
	elseif (z <= 1.25e+196)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -3e-51], t$95$1, If[LessEqual[z, 2.3e+16], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.25e+196], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000002e-51 or 1.2499999999999999e196 < z

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.2%

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

   if -3.00000000000000002e-51 < z < 2.3e16

   1. Initial program 91.8%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.1

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

   7. Applied rewrites 78.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 59.2%

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

   if 2.3e16 < z < 1.2499999999999999e196

   1. Initial program 56.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. div-sub N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.7

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

   8. Applied rewrites 63.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-51} \lor \neg \left(z \leq 6.4 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e-51) (not (<= z 6.4e+17)))
   (fma (- (- t x)) (/ (- y a) z) t)
   (fma (- y z) (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-51) || !(z <= 6.4e+17)) {
		tmp = fma(-(t - x), ((y - a) / z), t);
	} else {
		tmp = fma((y - z), ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e-51) || !(z <= 6.4e+17))
		tmp = fma(Float64(-Float64(t - x)), Float64(Float64(y - a) / z), t);
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e-51], N[Not[LessEqual[z, 6.4e+17]], $MachinePrecision]], N[((-N[(t - x), $MachinePrecision]) * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999997e-51 or 6.4e17 < z

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.8%

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

   if -3.4999999999999997e-51 < z < 6.4e17

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-51} \lor \neg \left(z \leq 6.4 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+92}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+103)
   t
   (if (<= z 2.55e+16)
     (fma y (/ t a) x)
     (if (<= z 1.14e+92) (* (/ (- x t) z) y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+103) {
		tmp = t;
	} else if (z <= 2.55e+16) {
		tmp = fma(y, (t / a), x);
	} else if (z <= 1.14e+92) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+103)
		tmp = t;
	elseif (z <= 2.55e+16)
		tmp = fma(y, Float64(t / a), x);
	elseif (z <= 1.14e+92)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+103], t, If[LessEqual[z, 2.55e+16], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.14e+92], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e103 or 1.13999999999999993e92 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 50.4%

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

   if -1.5e103 < z < 2.55e16

   1. Initial program 89.4%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.8

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 71.8

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

   7. Applied rewrites 71.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 55.5%

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

   if 2.55e16 < z < 1.13999999999999993e92

   1. Initial program 60.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. div-sub N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 57.0

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

   8. Applied rewrites 57.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+92}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-51} \lor \neg \left(z \leq 2.3 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e-51) (not (<= z 2.3e+16)))
   (fma (/ (- x t) z) y t)
   (fma y (/ t a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e-51) || !(z <= 2.3e+16)) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = fma(y, (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e-51) || !(z <= 2.3e+16))
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = fma(y, Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e-51], N[Not[LessEqual[z, 2.3e+16]], $MachinePrecision]], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e-51 or 2.3e16 < z

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. div-sub N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 68.4

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

   8. Applied rewrites 68.4%

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

   if -2.8e-51 < z < 2.3e16

   1. Initial program 91.8%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.1

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

   7. Applied rewrites 78.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 59.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-51} \lor \neg \left(z \leq 2.3 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+103) t (if (<= z 4.5e+94) (fma y (/ t a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+103) {
		tmp = t;
	} else if (z <= 4.5e+94) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+103)
		tmp = t;
	elseif (z <= 4.5e+94)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+103], t, If[LessEqual[z, 4.5e+94], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e103 or 4.49999999999999972e94 < z

   1. Initial program 34.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 50.7%

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

   if -1.5e103 < z < 4.49999999999999972e94

   1. Initial program 85.8%

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

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.5

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 65.3

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

   7. Applied rewrites 65.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 51.0%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+180) t (if (<= z -4.6e-179) (+ x t) (if (<= z 9.6e+26) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+180) {
		tmp = t;
	} else if (z <= -4.6e-179) {
		tmp = x + t;
	} else if (z <= 9.6e+26) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-6.5d+180)) then
        tmp = t
    else if (z <= (-4.6d-179)) then
        tmp = x + t
    else if (z <= 9.6d+26) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+180) {
		tmp = t;
	} else if (z <= -4.6e-179) {
		tmp = x + t;
	} else if (z <= 9.6e+26) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+180:
		tmp = t
	elif z <= -4.6e-179:
		tmp = x + t
	elif z <= 9.6e+26:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+180)
		tmp = t;
	elseif (z <= -4.6e-179)
		tmp = Float64(x + t);
	elseif (z <= 9.6e+26)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+180)
		tmp = t;
	elseif (z <= -4.6e-179)
		tmp = x + t;
	elseif (z <= 9.6e+26)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+180], t, If[LessEqual[z, -4.6e-179], N[(x + t), $MachinePrecision], If[LessEqual[z, 9.6e+26], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e180 or 9.60000000000000018e26 < z

   1. Initial program 38.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.5%

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

   if -6.5e180 < z < -4.59999999999999975e-179

   1. Initial program 74.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 17.4

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

   5. Applied rewrites 17.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + t \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto x + t \]

   if -4.59999999999999975e-179 < z < 9.60000000000000018e26

   1. Initial program 90.8%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 33.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -450000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -450000.0) t (if (<= z 9.6e+26) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -450000.0) {
		tmp = t;
	} else if (z <= 9.6e+26) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-450000.0d0)) then
        tmp = t
    else if (z <= 9.6d+26) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -450000.0) {
		tmp = t;
	} else if (z <= 9.6e+26) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -450000.0:
		tmp = t
	elif z <= 9.6e+26:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -450000.0)
		tmp = t;
	elseif (z <= 9.6e+26)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -450000.0)
		tmp = t;
	elseif (z <= 9.6e+26)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -450000.0], t, If[LessEqual[z, 9.6e+26], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e5 or 9.60000000000000018e26 < z

   1. Initial program 41.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 44.7%

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

   if -4.5e5 < z < 9.60000000000000018e26

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 32.9%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -450000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 24.9% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.9%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 26.9%

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

6. Final simplification 26.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer Target 1: 83.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 2025026 
(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))))