Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.8% → 92.3%

Time: 4.9s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

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

Initial Program: 80.8% accurate, 1.0× speedup

Math

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

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

Alternative 1: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y - z, x\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}, \frac{t \cdot \left(y - z\right)}{a - z}\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -1e+111)
     (fma t_1 (- y z) x)
     (if (<= t_2 -5e-302)
       (fma
        x
        (- (+ 1.0 (/ z (- a z))) (/ y (- a z)))
        (/ (* t (- y z)) (- a z)))
       (if (<= t_2 0.0) (fma x (* -1.0 (/ (- a y) z)) t) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -1e+111) {
		tmp = fma(t_1, (y - z), x);
	} else if (t_2 <= -5e-302) {
		tmp = fma(x, ((1.0 + (z / (a - z))) - (y / (a - z))), ((t * (y - z)) / (a - z)));
	} else if (t_2 <= 0.0) {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -1e+111)
		tmp = fma(t_1, Float64(y - z), x);
	elseif (t_2 <= -5e-302)
		tmp = fma(x, Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z))), Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	elseif (t_2 <= 0.0)
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+111], N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, -5e-302], N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999957e110

   1. Initial program 92.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.7

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

   3. Applied rewrites 92.7%

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

   if -9.99999999999999957e110 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000033e-302

   1. Initial program 87.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 94.1

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

   7. Applied rewrites 94.1%

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

   if -5.00000000000000033e-302 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 3.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 58.6

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

   7. Applied rewrites 58.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 66.6%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 96.3

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

   13. Applied rewrites 96.3%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.2%

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

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y - z, x\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, -\frac{\left(y - z\right) \cdot x}{a - z}\right) + x\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -1e+102)
     (fma t_1 (- y z) x)
     (if (<= t_2 -5e-302)
       (+ (fma (/ (- y z) (- a z)) t (- (/ (* (- y z) x) (- a z)))) x)
       (if (<= t_2 0.0) (fma x (* -1.0 (/ (- a y) z)) t) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -1e+102) {
		tmp = fma(t_1, (y - z), x);
	} else if (t_2 <= -5e-302) {
		tmp = fma(((y - z) / (a - z)), t, -(((y - z) * x) / (a - z))) + x;
	} else if (t_2 <= 0.0) {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -1e+102)
		tmp = fma(t_1, Float64(y - z), x);
	elseif (t_2 <= -5e-302)
		tmp = Float64(fma(Float64(Float64(y - z) / Float64(a - z)), t, Float64(-Float64(Float64(Float64(y - z) * x) / Float64(a - z)))) + x);
	elseif (t_2 <= 0.0)
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+102], N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, -5e-302], N[(N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + (-N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999977e101

   1. Initial program 92.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.8

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

   3. Applied rewrites 92.8%

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

   if -9.99999999999999977e101 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000033e-302

   1. Initial program 87.2%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 91.9%

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

   if -5.00000000000000033e-302 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 3.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 58.6

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

   7. Applied rewrites 58.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 66.6%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 96.3

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

   13. Applied rewrites 96.3%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.2%

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

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y - z, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -5e-241)
     (fma t_1 (- y z) x)
     (if (<= t_2 0.0) (fma x (* -1.0 (/ (- a y) z)) t) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -5e-241) {
		tmp = fma(t_1, (y - z), x);
	} else if (t_2 <= 0.0) {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -5e-241)
		tmp = fma(t_1, Float64(y - z), x);
	elseif (t_2 <= 0.0)
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-241], N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-241

   1. Initial program 91.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 91.5

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

   3. Applied rewrites 91.5%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 11.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 65.2%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 91.2

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

   13. Applied rewrites 91.2%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.2%

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

Alternative 4: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (fma t_1 (- y z) x))
        (t_3 (+ x (* (- y z) t_1))))
   (if (<= t_3 -5e-241)
     t_2
     (if (<= t_3 0.0) (fma x (* -1.0 (/ (- a y) z)) t) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = fma(t_1, (y - z), x);
	double t_3 = x + ((y - z) * t_1);
	double tmp;
	if (t_3 <= -5e-241) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = fma(t_1, Float64(y - z), x)
	t_3 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_3 <= -5e-241)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-241], t$95$2, If[LessEqual[t$95$3, 0.0], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-241 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 90.9

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

   3. Applied rewrites 90.9%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 11.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 65.2%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 91.2

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

   13. Applied rewrites 91.2%

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

Alternative 5: 80.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t - x\right) \cdot y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- t x) y) (- a z)))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (fma (/ t (- a z)) (- y z) x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-241)
       t_3
       (if (<= t_2 0.0)
         (fma x (* -1.0 (/ (- a y) z)) t)
         (if (<= t_2 2e+293) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / (a - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-241) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	} else if (t_2 <= 2e+293) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) * y) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-241)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	elseif (t_2 <= 2e+293)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-241], t$95$3, If[LessEqual[t$95$2, 0.0], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[t$95$2, 2e+293], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 1.9999999999999998e293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 86.6

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

   4. Applied rewrites 86.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-241 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999998e293

   1. Initial program 92.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.1

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

   3. Applied rewrites 92.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 77.1%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 11.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 65.2%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 91.2

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

   13. Applied rewrites 91.2%

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

Alternative 6: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;a \leq 4.05 \cdot 10^{-94}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-94)
   (fma (- t x) (/ (- y z) a) x)
   (if (<= a 4.05e-94)
     (+ (- (/ (* (- t x) (- y a)) z)) t)
     (fma (/ t (- a z)) (- y z) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-94) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (a <= 4.05e-94) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = fma((t / (a - z)), (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-94)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (a <= 4.05e-94)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-94], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 4.05e-94], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999997e-94

   1. Initial program 84.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 67.5

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

   4. Applied rewrites 67.5%

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

   if -9.4999999999999997e-94 < a < 4.0500000000000002e-94

   1. Initial program 72.8%

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

   2. Taylor expanded in z around inf

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

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

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

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

      6. 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. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 78.8%

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

   if 4.0500000000000002e-94 < a

   1. Initial program 85.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 85.6

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

   3. Applied rewrites 85.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 73.3%

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

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -460000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -1 \cdot \frac{a - y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -460000.0)
   (* t (/ (- y z) (- a z)))
   (if (<= z 9.6e-25)
     (+ x (* y (/ (- t x) (- a z))))
     (fma x (* -1.0 (/ (- a y) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -460000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 9.6e-25) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = fma(x, (-1.0 * ((a - y) / z)), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -460000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 9.6e-25)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = fma(x, Float64(-1.0 * Float64(Float64(a - y) / z)), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -460000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-25], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-1.0 * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e5

   1. Initial program 70.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 70.6

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

   3. Applied rewrites 70.6%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 60.7

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

   6. Applied rewrites 60.7%

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

   if -4.6e5 < z < 9.60000000000000037e-25

   1. Initial program 91.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 84.6%

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

   if 9.60000000000000037e-25 < z

   1. Initial program 71.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 68.8

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

   7. Applied rewrites 68.8%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 69.2%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 N/A

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

       2. lower-/.f64 N/A

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

       3. lift--.f64 63.7

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

   13. Applied rewrites 63.7%

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

Alternative 8: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t - x\right) \cdot y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-241}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-228}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- t x) y) (- a z)))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (fma (/ t (- a z)) (- y z) x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-241)
       t_3
       (if (<= t_2 4e-228) (fma x (/ y z) t) (if (<= t_2 2e+293) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) * y) / (a - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-241) {
		tmp = t_3;
	} else if (t_2 <= 4e-228) {
		tmp = fma(x, (y / z), t);
	} else if (t_2 <= 2e+293) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) * y) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-241)
		tmp = t_3;
	elseif (t_2 <= 4e-228)
		tmp = fma(x, Float64(y / z), t);
	elseif (t_2 <= 2e+293)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-241], t$95$3, If[LessEqual[t$95$2, 4e-228], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[t$95$2, 2e+293], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 1.9999999999999998e293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf

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

      1. sub-div N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 86.6

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

   4. Applied rewrites 86.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-241 or 4.00000000000000013e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999998e293

   1. Initial program 93.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 93.1

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

   3. Applied rewrites 93.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 77.8%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000013e-228

   1. Initial program 13.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 20.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 66.6

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

   7. Applied rewrites 66.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 62.9%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 60.8

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

   13. Applied rewrites 60.8%

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

Alternative 9: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.26 \cdot 10^{-100}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{elif}\;a \leq 2.02 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -9.5e-94)
     t_1
     (if (<= a 2.26e-100)
       (fma x (/ y z) t)
       (if (<= a 2.02e+93) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -9.5e-94) {
		tmp = t_1;
	} else if (a <= 2.26e-100) {
		tmp = fma(x, (y / z), t);
	} else if (a <= 2.02e+93) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -9.5e-94)
		tmp = t_1;
	elseif (a <= 2.26e-100)
		tmp = fma(x, Float64(y / z), t);
	elseif (a <= 2.02e+93)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9.5e-94], t$95$1, If[LessEqual[a, 2.26e-100], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[a, 2.02e+93], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999997e-94 or 2.01999999999999998e93 < a

   1. Initial program 86.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 72.6

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

   4. Applied rewrites 72.6%

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

   if -9.4999999999999997e-94 < a < 2.26e-100

   1. Initial program 72.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 57.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 78.3

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

   7. Applied rewrites 78.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 71.7%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 65.9

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

   13. Applied rewrites 65.9%

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

   if 2.26e-100 < a < 2.01999999999999998e93

   1. Initial program 79.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 79.4

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 53.7

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

   6. Applied rewrites 53.7%

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

Alternative 10: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ y z) t)))
   (if (<= z -2.1e+20)
     t_1
     (if (<= z -6.8e-65)
       (/ (* (- y z) t) (- a z))
       (if (<= z 4.5e-57) (fma (- t x) (/ y a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (y / z), t);
	double tmp;
	if (z <= -2.1e+20) {
		tmp = t_1;
	} else if (z <= -6.8e-65) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 4.5e-57) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(y / z), t)
	tmp = 0.0
	if (z <= -2.1e+20)
		tmp = t_1;
	elseif (z <= -6.8e-65)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 4.5e-57)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -2.1e+20], t$95$1, If[LessEqual[z, -6.8e-65], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-57], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e20 or 4.49999999999999973e-57 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 58.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 68.1

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

   7. Applied rewrites 68.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 69.5%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 56.4

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

   13. Applied rewrites 56.4%

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

   if -2.1e20 < z < -6.79999999999999973e-65

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 43.2

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

   4. Applied rewrites 43.2%

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

   if -6.79999999999999973e-65 < z < 4.49999999999999973e-57

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 79.8%

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

Alternative 11: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e-65)
   (* t (/ (- y z) (- a z)))
   (if (<= z 4.5e-57) (fma (- t x) (/ y a) x) (fma x (/ y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-65) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.5e-57) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = fma(x, (y / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e-65)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 4.5e-57)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = fma(x, Float64(y / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e-65], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-57], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999973e-65

   1. Initial program 74.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 74.2

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

   3. Applied rewrites 74.2%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 58.0

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

   6. Applied rewrites 58.0%

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

   if -6.79999999999999973e-65 < z < 4.49999999999999973e-57

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 79.8%

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

   if 4.49999999999999973e-57 < z

   1. Initial program 73.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 70.9

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

   7. Applied rewrites 70.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 67.9%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 54.2

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

   13. Applied rewrites 54.2%

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

Alternative 12: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ y z) t)))
   (if (<= z -1.35e-28) t_1 (if (<= z 4.5e-57) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (y / z), t);
	double tmp;
	if (z <= -1.35e-28) {
		tmp = t_1;
	} else if (z <= 4.5e-57) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(y / z), t)
	tmp = 0.0
	if (z <= -1.35e-28)
		tmp = t_1;
	elseif (z <= 4.5e-57)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -1.35e-28], t$95$1, If[LessEqual[z, 4.5e-57], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-28 or 4.49999999999999973e-57 < z

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 69.5

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

   7. Applied rewrites 69.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 69.0%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 55.2

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

   13. Applied rewrites 55.2%

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

   if -1.3499999999999999e-28 < z < 4.49999999999999973e-57

   1. Initial program 91.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 81.2

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

   4. Applied rewrites 81.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 78.2%

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

Alternative 13: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ y z) t)))
   (if (<= z -1.35e-28) t_1 (if (<= z 4.5e-57) (fma y (/ (- t x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (y / z), t);
	double tmp;
	if (z <= -1.35e-28) {
		tmp = t_1;
	} else if (z <= 4.5e-57) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(y / z), t)
	tmp = 0.0
	if (z <= -1.35e-28)
		tmp = t_1;
	elseif (z <= 4.5e-57)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -1.35e-28], t$95$1, If[LessEqual[z, 4.5e-57], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-28 or 4.49999999999999973e-57 < z

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 69.5

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

   7. Applied rewrites 69.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 69.0%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 55.2

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

   13. Applied rewrites 55.2%

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

   if -1.3499999999999999e-28 < z < 4.49999999999999973e-57

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   3. 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. lift--.f64 75.7

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

   4. Applied rewrites 75.7%

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

Alternative 14: 59.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (/ y a) x)))
   (if (<= a -5.6e+51) t_1 (if (<= a 2.02e+93) (fma x (/ y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, (y / a), x);
	double tmp;
	if (a <= -5.6e+51) {
		tmp = t_1;
	} else if (a <= 2.02e+93) {
		tmp = fma(x, (y / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(y / a), x)
	tmp = 0.0
	if (a <= -5.6e+51)
		tmp = t_1;
	elseif (a <= 2.02e+93)
		tmp = fma(x, Float64(y / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.6e+51], t$95$1, If[LessEqual[a, 2.02e+93], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000009e51 or 2.01999999999999998e93 < a

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 72.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 63.9%

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

   if -5.60000000000000009e51 < a < 2.01999999999999998e93

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 78.7

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

   7. Applied rewrites 78.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 68.8%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 56.2

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

   13. Applied rewrites 56.2%

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

Alternative 15: 53.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e+51) x (if (<= a 3.3e+93) (fma x (/ y z) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+51) {
		tmp = x;
	} else if (a <= 3.3e+93) {
		tmp = fma(x, (y / z), t);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+51)
		tmp = x;
	elseif (a <= 3.3e+93)
		tmp = fma(x, Float64(y / z), t);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+51], x, If[LessEqual[a, 3.3e+93], N[(x * N[(y / z), $MachinePrecision] + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5999999999999994e51 or 3.30000000000000009e93 < a

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 48.4%

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

   if -8.5999999999999994e51 < a < 3.30000000000000009e93

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 78.7

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

   7. Applied rewrites 78.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 68.8%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 56.2

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

   13. Applied rewrites 56.2%

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

Alternative 16: 43.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y}{z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) z)) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-207)
       (fma x 1.0 t)
       (if (<= t_2 2e-265) t (if (<= t_2 5e+297) (fma x 1.0 t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / z;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-207) {
		tmp = fma(x, 1.0, t);
	} else if (t_2 <= 2e-265) {
		tmp = t;
	} else if (t_2 <= 5e+297) {
		tmp = fma(x, 1.0, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / z)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-207)
		tmp = fma(x, 1.0, t);
	elseif (t_2 <= 2e-265)
		tmp = t;
	elseif (t_2 <= 5e+297)
		tmp = fma(x, 1.0, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-207], N[(x * 1.0 + t), $MachinePrecision], If[LessEqual[t$95$2, 2e-265], t, If[LessEqual[t$95$2, 5e+297], N[(x * 1.0 + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 4.9999999999999998e297 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. sub-div N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 55.9

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

   4. Applied rewrites 55.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.2

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

   7. Applied rewrites 41.2%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999985e-207 or 1.99999999999999997e-265 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e297

   1. Initial program 93.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 74.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.0

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

   7. Applied rewrites 79.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.8%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 45.5%

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]

   if -1.99999999999999985e-207 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999997e-265

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 36.5%

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

Alternative 17: 38.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+202}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, t\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.9e+202)
   (/ (* t y) a)
   (if (<= y 2.5e-8) (fma x 1.0 t) (if (<= y 6.2e+118) t (* (/ y z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.9e+202) {
		tmp = (t * y) / a;
	} else if (y <= 2.5e-8) {
		tmp = fma(x, 1.0, t);
	} else if (y <= 6.2e+118) {
		tmp = t;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.9e+202)
		tmp = Float64(Float64(t * y) / a);
	elseif (y <= 2.5e-8)
		tmp = fma(x, 1.0, t);
	elseif (y <= 6.2e+118)
		tmp = t;
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.9e+202], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.5e-8], N[(x * 1.0 + t), $MachinePrecision], If[LessEqual[y, 6.2e+118], t, N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9e202

   1. Initial program 91.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 40.2

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

   4. Applied rewrites 40.2%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 28.8

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

   7. Applied rewrites 28.8%

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

   if -1.9e202 < y < 2.4999999999999999e-8

   1. Initial program 76.9%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.3

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

   7. Applied rewrites 79.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 64.7%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 42.6%

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]

   if 2.4999999999999999e-8 < y < 6.19999999999999973e118

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 25.6%

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

   if 6.19999999999999973e118 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. sub-div N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 48.6

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

   4. Applied rewrites 48.6%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 33.1

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

   7. Applied rewrites 33.1%

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

Alternative 18: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, t\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 1, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-207) (fma x 1.0 t) (if (<= t_1 2e-265) t (fma x 1.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-207) {
		tmp = fma(x, 1.0, t);
	} else if (t_1 <= 2e-265) {
		tmp = t;
	} else {
		tmp = fma(x, 1.0, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-207)
		tmp = fma(x, 1.0, t);
	elseif (t_1 <= 2e-265)
		tmp = t;
	else
		tmp = fma(x, 1.0, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-207], N[(x * 1.0 + t), $MachinePrecision], If[LessEqual[t$95$1, 2e-265], t, N[(x * 1.0 + t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999985e-207 or 1.99999999999999997e-265 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 80.1

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

   7. Applied rewrites 80.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.2%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 38.8%

       \[\leadsto \mathsf{fma}\left(x, 1, t\right) \]

   if -1.99999999999999985e-207 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999997e-265

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 36.5%

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

Alternative 19: 38.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4e+26) x (if (<= a 2.95e+93) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e+26) {
		tmp = x;
	} else if (a <= 2.95e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	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 (a <= (-4d+26)) then
        tmp = x
    else if (a <= 2.95d+93) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e+26) {
		tmp = x;
	} else if (a <= 2.95e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4e+26:
		tmp = x
	elif a <= 2.95e+93:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4e+26)
		tmp = x;
	elseif (a <= 2.95e+93)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4e+26)
		tmp = x;
	elseif (a <= 2.95e+93)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4e+26], x, If[LessEqual[a, 2.95e+93], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.00000000000000019e26 or 2.95000000000000004e93 < a

   1. Initial program 89.0%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 47.1%

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

   if -4.00000000000000019e26 < a < 2.95000000000000004e93

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 32.6%

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

Alternative 20: 25.1% accurate, 17.9× 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 80.8%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.1%

   \[\leadsto \color{blue}{t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025112 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))