Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 88.0%

Time: 4.8s

Alternatives: 18

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: 80.0% 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: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-108}:\\ \;\;\;\;\left(-x\right) \cdot \left(\mathsf{fma}\left(\frac{\frac{\left(y - z\right) \cdot t}{x}}{a - z}, -1, \frac{y}{a - z}\right) - \left(\frac{z}{a - z} + 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -4e-71)
     t_2
     (if (<= t_3 4e-108)
       (*
        (- x)
        (-
         (fma (/ (/ (* (- y z) t) x) (- a z)) -1.0 (/ y (- a z)))
         (+ (/ z (- a z)) 1.0)))
       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 <= -4e-71) {
		tmp = t_2;
	} else if (t_3 <= 4e-108) {
		tmp = -x * (fma(((((y - z) * t) / x) / (a - z)), -1.0, (y / (a - z))) - ((z / (a - z)) + 1.0));
	} 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 <= -4e-71)
		tmp = t_2;
	elseif (t_3 <= 4e-108)
		tmp = Float64(Float64(-x) * Float64(fma(Float64(Float64(Float64(Float64(y - z) * t) / x) / Float64(a - z)), -1.0, Float64(y / Float64(a - z))) - Float64(Float64(z / Float64(a - z)) + 1.0)));
	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, -4e-71], t$95$2, If[LessEqual[t$95$3, 4e-108], N[((-x) * N[(N[(N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * -1.0 + N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $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)))) < -3.9999999999999997e-71 or 4.00000000000000016e-108 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. 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 93.4

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

   4. Applied rewrites 93.4%

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

   if -3.9999999999999997e-71 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000016e-108

   1. Initial program 37.7%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 70.9%

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

Alternative 2: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-203)
     t_2
     (if (<= t_3 2e-252) (fma (/ (* (- t x) (- y a)) z) -1.0 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-203) {
		tmp = t_2;
	} else if (t_3 <= 2e-252) {
		tmp = fma((((t - x) * (y - a)) / z), -1.0, 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-203)
		tmp = t_2;
	elseif (t_3 <= 2e-252)
		tmp = fma(Float64(Float64(Float64(t - x) * Float64(y - a)) / z), -1.0, 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-203], t$95$2, If[LessEqual[t$95$3, 2e-252], N[(N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 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)))) < -5.0000000000000002e-203 or 1.99999999999999989e-252 < (+.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. Add Preprocessing
   3. 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 91.7

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

   4. Applied rewrites 91.7%

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

   if -5.0000000000000002e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999989e-252

   1. Initial program 14.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. 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. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 73.3%

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

Alternative 3: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot y}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-203)
     t_2
     (if (<= t_3 2e-252) (fma (/ (* (- t x) y) z) -1.0 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-203) {
		tmp = t_2;
	} else if (t_3 <= 2e-252) {
		tmp = fma((((t - x) * y) / z), -1.0, 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-203)
		tmp = t_2;
	elseif (t_3 <= 2e-252)
		tmp = fma(Float64(Float64(Float64(t - x) * y) / z), -1.0, 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-203], t$95$2, If[LessEqual[t$95$3, 2e-252], N[(N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 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)))) < -5.0000000000000002e-203 or 1.99999999999999989e-252 < (+.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. Add Preprocessing
   3. 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 91.7

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

   4. Applied rewrites 91.7%

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

   if -5.0000000000000002e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999989e-252

   1. Initial program 14.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. 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. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 53.6%

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

Alternative 4: 37.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-203}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-203) (+ x t) (if (<= t_1 0.0) t (+ x 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 <= -5e-203) {
		tmp = x + t;
	} else if (t_1 <= 0.0) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-203)) then
        tmp = x + t
    else if (t_1 <= 0.0d0) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-203) {
		tmp = x + t;
	} else if (t_1 <= 0.0) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-203:
		tmp = x + t
	elif t_1 <= 0.0:
		tmp = t
	else:
		tmp = x + 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 <= -5e-203)
		tmp = Float64(x + t);
	elseif (t_1 <= 0.0)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-203)
		tmp = x + t;
	elseif (t_1 <= 0.0)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = 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, -5e-203], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 0.0], t, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000002e-203 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf

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

      1. lift--.f64 21.2

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

   5. Applied rewrites 21.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.3%

      \[\leadsto x + t \]

   if -5.0000000000000002e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 11.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 34.8%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -t \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-242}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y, x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* t (/ z (- a z))))))
   (if (<= z -4.8e+136)
     t_1
     (if (<= z -9e-242)
       (fma (/ (- t x) (- a z)) y x)
       (if (<= z 8e+152) (fma (- t x) (/ (- y z) a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t * (z / (a - z)));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_1;
	} else if (z <= -9e-242) {
		tmp = fma(((t - x) / (a - z)), y, x);
	} else if (z <= 8e+152) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t * Float64(z / Float64(a - z))))
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t_1;
	elseif (z <= -9e-242)
		tmp = fma(Float64(Float64(t - x) / Float64(a - z)), y, x);
	elseif (z <= 8e+152)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -4.8e+136], t$95$1, If[LessEqual[z, -9e-242], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 8e+152], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000001e136 or 8.0000000000000004e152 < z

   1. Initial program 57.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 36.4

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

   5. Applied rewrites 36.4%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 61.7

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

   8. Applied rewrites 61.7%

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

   if -4.8000000000000001e136 < z < -8.9999999999999997e-242

   1. Initial program 86.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. 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 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 70.8%

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

   if -8.9999999999999997e-242 < z < 8.0000000000000004e152

   1. Initial program 88.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 70.6

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

   5. Applied rewrites 70.6%

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

Alternative 6: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-37}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -4.2e-85)
     t_1
     (if (<= a -7.8e-296)
       (/ (* (- t x) y) (- a z))
       (if (<= a 1.65e-37) (/ (* (- y z) t) (- 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 <= -4.2e-85) {
		tmp = t_1;
	} else if (a <= -7.8e-296) {
		tmp = ((t - x) * y) / (a - z);
	} else if (a <= 1.65e-37) {
		tmp = ((y - z) * t) / (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 <= -4.2e-85)
		tmp = t_1;
	elseif (a <= -7.8e-296)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	elseif (a <= 1.65e-37)
		tmp = Float64(Float64(Float64(y - z) * t) / 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, -4.2e-85], t$95$1, If[LessEqual[a, -7.8e-296], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-37], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2e-85 or 1.64999999999999991e-37 < a

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 70.7

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

   5. Applied rewrites 70.7%

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

   if -4.2e-85 < a < -7.80000000000000021e-296

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf

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

      1. 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 54.4

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

   5. Applied rewrites 54.4%

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

   if -7.80000000000000021e-296 < a < 1.64999999999999991e-37

   1. Initial program 71.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 50.9

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

   5. Applied rewrites 50.9%

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

Alternative 7: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{if}\;a \leq -150000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ y a) x)))
   (if (<= a -150000000.0)
     t_1
     (if (<= a -7.8e-296)
       (/ (* (- t x) y) (- a z))
       (if (<= a 2.8e-37) (/ (* (- y z) t) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), (y / a), x);
	double tmp;
	if (a <= -150000000.0) {
		tmp = t_1;
	} else if (a <= -7.8e-296) {
		tmp = ((t - x) * y) / (a - z);
	} else if (a <= 2.8e-37) {
		tmp = ((y - z) * t) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(y / a), x)
	tmp = 0.0
	if (a <= -150000000.0)
		tmp = t_1;
	elseif (a <= -7.8e-296)
		tmp = Float64(Float64(Float64(t - x) * y) / Float64(a - z));
	elseif (a <= 2.8e-37)
		tmp = Float64(Float64(Float64(y - z) * t) / 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[(y / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -150000000.0], t$95$1, If[LessEqual[a, -7.8e-296], N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-37], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5e8 or 2.8000000000000001e-37 < a

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 66.0%

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

   if -1.5e8 < a < -7.80000000000000021e-296

   1. Initial program 71.9%

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

   3. Taylor expanded in y around inf

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

      1. 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 52.4

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

   5. Applied rewrites 52.4%

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

   if -7.80000000000000021e-296 < a < 2.8000000000000001e-37

   1. Initial program 71.8%

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

   3. Taylor expanded in x around 0

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

      1. 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 50.8

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

   5. Applied rewrites 50.8%

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

Alternative 8: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -t \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-25}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* t (/ z (- a z))))))
   (if (<= z -3.8e+159)
     t_1
     (if (<= z -9.8e-25)
       (* (- y z) (/ t (- a z)))
       (if (<= z 8e+152) (fma (- t x) (/ y a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t * (z / (a - z)));
	double tmp;
	if (z <= -3.8e+159) {
		tmp = t_1;
	} else if (z <= -9.8e-25) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 8e+152) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t * Float64(z / Float64(a - z))))
	tmp = 0.0
	if (z <= -3.8e+159)
		tmp = t_1;
	elseif (z <= -9.8e-25)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 8e+152)
		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[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -3.8e+159], t$95$1, If[LessEqual[z, -9.8e-25], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+152], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.79999999999999965e159 or 8.0000000000000004e152 < z

   1. Initial program 57.3%

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

   3. Taylor expanded in x around 0

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

      1. 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 36.3

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

   5. Applied rewrites 36.3%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 63.0

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

   8. Applied rewrites 63.0%

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

   if -3.79999999999999965e159 < z < -9.7999999999999998e-25

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0

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

      1. 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

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

   5. Applied rewrites 43.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 49.5

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

   7. Applied rewrites 49.5%

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

   if -9.7999999999999998e-25 < z < 8.0000000000000004e152

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 67.1%

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

Alternative 9: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot y}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.3e-31)
   (fma (- t x) (/ (- y z) a) x)
   (if (<= a 5e-71)
     (fma (/ (* (- t x) y) z) -1.0 t)
     (+ x (* (- y z) (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e-31) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (a <= 5e-71) {
		tmp = fma((((t - x) * y) / z), -1.0, t);
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.3e-31)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (a <= 5e-71)
		tmp = fma(Float64(Float64(Float64(t - x) * y) / z), -1.0, t);
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.3e-31], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 5e-71], N[(N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2999999999999999e-31

   1. Initial program 86.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 73.4

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

   5. Applied rewrites 73.4%

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

   if -3.2999999999999999e-31 < a < 4.99999999999999998e-71

   1. Initial program 71.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. 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. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 72.9%

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

   if 4.99999999999999998e-71 < a

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 73.5%

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

Alternative 10: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot y}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -3.3e-31)
     t_1
     (if (<= a 3.4e-65) (fma (/ (* (- t x) y) z) -1.0 t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -3.3e-31) {
		tmp = t_1;
	} else if (a <= 3.4e-65) {
		tmp = fma((((t - x) * y) / z), -1.0, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -3.3e-31)
		tmp = t_1;
	elseif (a <= 3.4e-65)
		tmp = fma(Float64(Float64(Float64(t - x) * y) / z), -1.0, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.3e-31], t$95$1, If[LessEqual[a, 3.4e-65], N[(N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2999999999999999e-31 or 3.39999999999999987e-65 < a

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 71.6

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

   5. Applied rewrites 71.6%

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

   if -3.2999999999999999e-31 < a < 3.39999999999999987e-65

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. 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. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 72.8%

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

Alternative 11: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -t \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* t (/ z (- a z))))))
   (if (<= z -4.8e+136) t_1 (if (<= z 8e+152) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t * (z / (a - z)));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_1;
	} else if (z <= 8e+152) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t * Float64(z / Float64(a - z))))
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t_1;
	elseif (z <= 8e+152)
		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[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -4.8e+136], t$95$1, If[LessEqual[z, 8e+152], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e136 or 8.0000000000000004e152 < z

   1. Initial program 57.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 36.4

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

   5. Applied rewrites 36.4%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 61.7

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

   8. Applied rewrites 61.7%

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

   if -4.8000000000000001e136 < z < 8.0000000000000004e152

   1. Initial program 87.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 67.0

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 61.9%

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

Alternative 12: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+136) t (if (<= z 8e+152) (fma (- t x) (/ y a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t;
	} else if (z <= 8e+152) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t;
	elseif (z <= 8e+152)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+136], t, If[LessEqual[z, 8e+152], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e136 or 8.0000000000000004e152 < z

   1. Initial program 57.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 57.0%

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

   if -4.8000000000000001e136 < z < 8.0000000000000004e152

   1. Initial program 87.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. 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 67.0

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 61.9%

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

Alternative 13: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+136) t (if (<= z 8e+152) (fma y (/ (- t x) a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t;
	} else if (z <= 8e+152) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t;
	elseif (z <= 8e+152)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+136], t, If[LessEqual[z, 8e+152], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e136 or 8.0000000000000004e152 < z

   1. Initial program 57.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 57.0%

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

   if -4.8000000000000001e136 < z < 8.0000000000000004e152

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. 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 60.6

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

   5. Applied rewrites 60.6%

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

Alternative 14: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+192}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+136)
   t
   (if (<= z 1.6e+36) (fma y (/ t a) x) (if (<= z 1.9e+192) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t;
	} else if (z <= 1.6e+36) {
		tmp = fma(y, (t / a), x);
	} else if (z <= 1.9e+192) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t;
	elseif (z <= 1.6e+36)
		tmp = fma(y, Float64(t / a), x);
	elseif (z <= 1.9e+192)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+136], t, If[LessEqual[z, 1.6e+36], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.9e+192], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000001e136 or 1.9e192 < z

   1. Initial program 55.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 58.6%

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

   if -4.8000000000000001e136 < z < 1.5999999999999999e36

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. 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 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.0%

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

   if 1.5999999999999999e36 < z < 1.9e192

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf

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

      1. lift--.f64 26.3

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

   5. Applied rewrites 26.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.5%

      \[\leadsto x + t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.2e+209)
   (* t (/ y a))
   (if (<= y 1.2e+101) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+209) {
		tmp = t * (y / a);
	} else if (y <= 1.2e+101) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	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 (y <= (-4.2d+209)) then
        tmp = t * (y / a)
    else if (y <= 1.2d+101) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+209) {
		tmp = t * (y / a);
	} else if (y <= 1.2e+101) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.2e+209:
		tmp = t * (y / a)
	elif y <= 1.2e+101:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.2e+209)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 1.2e+101)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.2e+209)
		tmp = t * (y / a);
	elseif (y <= 1.2e+101)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.2e+209], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+101], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e209

   1. Initial program 91.9%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 60.4%

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

   6. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 43.7

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

   8. Applied rewrites 43.7%

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

   9. Taylor expanded in z around 0

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

       1. lower-/.f64 39.0

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

   11. Applied rewrites 39.0%

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

   if -4.2e209 < y < 1.19999999999999994e101

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. lift--.f64 22.6

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

   5. Applied rewrites 22.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.4%

      \[\leadsto x + t \]

   if 1.19999999999999994e101 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. 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. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 45.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 32.4

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

   8. Applied rewrites 32.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 32.0%

       \[\leadsto x \cdot \frac{y}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -4.2e+209) t_1 (if (<= y 7.8e+96) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -4.2e+209) {
		tmp = t_1;
	} else if (y <= 7.8e+96) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-4.2d+209)) then
        tmp = t_1
    else if (y <= 7.8d+96) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -4.2e+209) {
		tmp = t_1;
	} else if (y <= 7.8e+96) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -4.2e+209:
		tmp = t_1
	elif y <= 7.8e+96:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -4.2e+209)
		tmp = t_1;
	elseif (y <= 7.8e+96)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -4.2e+209)
		tmp = t_1;
	elseif (y <= 7.8e+96)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+209], t$95$1, If[LessEqual[y, 7.8e+96], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e209 or 7.8e96 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 44.3

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

   8. Applied rewrites 44.3%

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

   9. Taylor expanded in z around 0

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

       1. lower-/.f64 35.5

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

   11. Applied rewrites 35.5%

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

   if -4.2e209 < y < 7.8e96

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. lift--.f64 22.6

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

   5. Applied rewrites 22.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.5%

      \[\leadsto x + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 38.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e-25) t (if (<= z 3.7e+36) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-25) {
		tmp = t;
	} else if (z <= 3.7e+36) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d-25)) then
        tmp = t
    else if (z <= 3.7d+36) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-25) {
		tmp = t;
	} else if (z <= 3.7e+36) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e-25:
		tmp = t
	elif z <= 3.7e+36:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e-25)
		tmp = t;
	elseif (z <= 3.7e+36)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e-25)
		tmp = t;
	elseif (z <= 3.7e+36)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e-25], t, If[LessEqual[z, 3.7e+36], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-25 or 3.70000000000000029e36 < z

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 42.4%

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

   if -2.6e-25 < z < 3.70000000000000029e36

   1. Initial program 91.1%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 34.6%

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

Alternative 18: 25.1% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

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 80.0%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 25.1%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025089 
(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)))))