Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.0% → 89.6%

Time: 6.6s

Alternatives: 15

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: 81.0% 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: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-226}:\\ \;\;\;\;t - 1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-233)
     t_2
     (if (<= t_3 5e-226)
       (- t (* 1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       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-233) {
		tmp = t_2;
	} else if (t_3 <= 5e-226) {
		tmp = t - (1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} 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-233)
		tmp = t_2;
	elseif (t_3 <= 5e-226)
		tmp = Float64(t - Float64(1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	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-233], t$95$2, If[LessEqual[t$95$3, 5e-226], N[(t - N[(1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $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)))) < -5.00000000000000012e-233 or 4.9999999999999998e-226 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.3

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

   3. Applied rewrites 92.3%

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

   if -5.00000000000000012e-233 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-226

   1. Initial program 15.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 15.5

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

   3. Applied rewrites 15.5%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 73.9

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

   6. Applied rewrites 73.9%

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

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-226}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}, -1, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-233)
     t_2
     (if (<= t_3 5e-226) (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-233) {
		tmp = t_2;
	} else if (t_3 <= 5e-226) {
		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-233)
		tmp = t_2;
	elseif (t_3 <= 5e-226)
		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-233], t$95$2, If[LessEqual[t$95$3, 5e-226], 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)))) < -5.00000000000000012e-233 or 4.9999999999999998e-226 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.3

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

   3. Applied rewrites 92.3%

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

   if -5.00000000000000012e-233 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-226

   1. Initial program 15.0%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. *-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

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

   4. Applied rewrites 73.9%

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

Alternative 3: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-226}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-233) t_2 (if (<= t_3 5e-226) (fma (/ (- t x) z) a 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-233) {
		tmp = t_2;
	} else if (t_3 <= 5e-226) {
		tmp = fma(((t - x) / z), a, 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-233)
		tmp = t_2;
	elseif (t_3 <= 5e-226)
		tmp = fma(Float64(Float64(t - x) / z), a, 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-233], t$95$2, If[LessEqual[t$95$3, 5e-226], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + 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)))) < -5.00000000000000012e-233 or 4.9999999999999998e-226 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.3

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

   3. Applied rewrites 92.3%

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

   if -5.00000000000000012e-233 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-226

   1. Initial program 15.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 15.5

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

   3. Applied rewrites 15.5%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 73.9

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-div N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 61.4

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

   9. Applied rewrites 61.4%

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

Alternative 4: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{z}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, t\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - t\_1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) z)))
   (if (<= z -5.7e+172)
     (fma t_1 a t)
     (if (<= z -2e-60)
       (fma (/ t (- a z)) (- y z) x)
       (if (<= z 7.5e+116) (+ x (* y (/ (- t x) (- a z)))) (- t (* t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / z;
	double tmp;
	if (z <= -5.7e+172) {
		tmp = fma(t_1, a, t);
	} else if (z <= -2e-60) {
		tmp = fma((t / (a - z)), (y - z), x);
	} else if (z <= 7.5e+116) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t - (t_1 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / z)
	tmp = 0.0
	if (z <= -5.7e+172)
		tmp = fma(t_1, a, t);
	elseif (z <= -2e-60)
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), x);
	elseif (z <= 7.5e+116)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(t_1 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.7e+172], N[(t$95$1 * a + t), $MachinePrecision], If[LessEqual[z, -2e-60], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 7.5e+116], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7e172

   1. Initial program 57.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 58.0

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

   3. Applied rewrites 58.0%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 64.9

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

   6. Applied rewrites 64.9%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-div N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 67.1

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

   9. Applied rewrites 67.1%

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

   if -5.7e172 < z < -1.9999999999999999e-60

   1. Initial program 83.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 83.1

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

   3. Applied rewrites 83.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 65.3%

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

   if -1.9999999999999999e-60 < z < 7.5e116

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 80.8%

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

   if 7.5e116 < z

   1. Initial program 62.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 62.4

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 63.1

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 73.8

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

   9. Applied rewrites 73.8%

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

Alternative 5: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- a z)) (- y z) x)))
   (if (<= a -6.5e+19) t_1 (if (<= a 7.5e-99) (- t (* (/ (- t x) z) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (a <= -6.5e+19) {
		tmp = t_1;
	} else if (a <= 7.5e-99) {
		tmp = t - (((t - x) / z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (a <= -6.5e+19)
		tmp = t_1;
	elseif (a <= 7.5e-99)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -6.5e+19], t$95$1, If[LessEqual[a, 7.5e-99], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5e19 or 7.4999999999999999e-99 < a

   1. Initial program 86.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 86.4

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

   3. Applied rewrites 86.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 75.0%

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

   if -6.5e19 < a < 7.4999999999999999e-99

   1. Initial program 74.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 74.1

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

   3. Applied rewrites 74.1%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 74.5

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

   6. Applied rewrites 74.5%

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

   7. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 75.1

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

   9. Applied rewrites 75.1%

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

Alternative 6: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -1e+37) t_1 (if (<= a 2.2e+27) (- t (* (/ (- t x) z) y)) 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 <= -1e+37) {
		tmp = t_1;
	} else if (a <= 2.2e+27) {
		tmp = t - (((t - x) / z) * y);
	} 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 <= -1e+37)
		tmp = t_1;
	elseif (a <= 2.2e+27)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * y));
	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, -1e+37], t$95$1, If[LessEqual[a, 2.2e+27], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999954e36 or 2.1999999999999999e27 < a

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 78.1

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

   4. Applied rewrites 78.1%

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

   if -9.99999999999999954e36 < a < 2.1999999999999999e27

   1. Initial program 74.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 74.8

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

   3. Applied rewrites 74.8%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 69.7

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

   6. Applied rewrites 69.7%

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

   7. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 70.2

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

   9. Applied rewrites 70.2%

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

Alternative 7: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-232}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-254}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+172)
   t
   (if (<= z -1.8e-232)
     (+ x t)
     (if (<= z 5.5e-254) (/ (* t y) a) (if (<= z 7.5e+116) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+172) {
		tmp = t;
	} else if (z <= -1.8e-232) {
		tmp = x + t;
	} else if (z <= 5.5e-254) {
		tmp = (t * y) / a;
	} else if (z <= 7.5e+116) {
		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 <= (-1.85d+172)) then
        tmp = t
    else if (z <= (-1.8d-232)) then
        tmp = x + t
    else if (z <= 5.5d-254) then
        tmp = (t * y) / a
    else if (z <= 7.5d+116) 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 <= -1.85e+172) {
		tmp = t;
	} else if (z <= -1.8e-232) {
		tmp = x + t;
	} else if (z <= 5.5e-254) {
		tmp = (t * y) / a;
	} else if (z <= 7.5e+116) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+172:
		tmp = t
	elif z <= -1.8e-232:
		tmp = x + t
	elif z <= 5.5e-254:
		tmp = (t * y) / a
	elif z <= 7.5e+116:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+172)
		tmp = t;
	elseif (z <= -1.8e-232)
		tmp = Float64(x + t);
	elseif (z <= 5.5e-254)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= 7.5e+116)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+172)
		tmp = t;
	elseif (z <= -1.8e-232)
		tmp = x + t;
	elseif (z <= 5.5e-254)
		tmp = (t * y) / a;
	elseif (z <= 7.5e+116)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+172], t, If[LessEqual[z, -1.8e-232], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.5e-254], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 7.5e+116], x, t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.84999999999999986e172 or 7.5e116 < z

   1. Initial program 60.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 56.6%

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

   if -1.84999999999999986e172 < z < -1.80000000000000008e-232

   1. Initial program 86.6%

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

   2. Taylor expanded in z around inf

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

      1. lift--.f64 14.3

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

   4. Applied rewrites 14.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 32.6%

      \[\leadsto x + t \]

   if -1.80000000000000008e-232 < z < 5.4999999999999999e-254

   1. Initial program 92.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 37.4

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

   4. Applied rewrites 37.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.2

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

   7. Applied rewrites 35.2%

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

   if 5.4999999999999999e-254 < z < 7.5e116

   1. Initial program 88.9%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 29.8%

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

Alternative 8: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+37)
   (fma (- t x) (/ y a) x)
   (if (<= a 2.2e+27) (- t (* (/ (- t x) z) y)) (fma y (/ (- t x) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+37) {
		tmp = fma((t - x), (y / a), x);
	} else if (a <= 2.2e+27) {
		tmp = t - (((t - x) / z) * y);
	} else {
		tmp = fma(y, ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+37)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	elseif (a <= 2.2e+27)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * y));
	else
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+37], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2.2e+27], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e37

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 68.7

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

   4. Applied rewrites 68.7%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 69.7

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

   6. Applied rewrites 69.7%

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

   if -1.2e37 < a < 2.1999999999999999e27

   1. Initial program 74.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 74.8

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

   3. Applied rewrites 74.8%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 69.7

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

   6. Applied rewrites 69.7%

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

   7. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. sub-div N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 70.2

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

   9. Applied rewrites 70.2%

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

   if 2.1999999999999999e27 < a

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 68.8

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

   4. Applied rewrites 68.8%

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

Alternative 9: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+131)
   (fma (/ (- t x) z) a t)
   (if (<= z 7.5e-44) (fma (- t x) (/ y a) x) (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+131) {
		tmp = fma(((t - x) / z), a, t);
	} else if (z <= 7.5e-44) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+131)
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	elseif (z <= 7.5e-44)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+131], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision], If[LessEqual[z, 7.5e-44], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999971e131

   1. Initial program 61.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 61.8

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

   3. Applied rewrites 61.8%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 63.1

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-div N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 62.5

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

   9. Applied rewrites 62.5%

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

   if -4.19999999999999971e131 < z < 7.50000000000000008e-44

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 67.7

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

   4. Applied rewrites 67.7%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 69.6

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

   6. Applied rewrites 69.6%

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

   if 7.50000000000000008e-44 < z

   1. Initial program 72.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 72.2

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

   3. Applied rewrites 72.2%

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

   4. Taylor expanded in t around inf

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

      1. sub-div N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 10: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) z) a t)))
   (if (<= z -4.2e+131) t_1 (if (<= z 4e+118) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / z), a, t);
	double tmp;
	if (z <= -4.2e+131) {
		tmp = t_1;
	} else if (z <= 4e+118) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / z), a, t)
	tmp = 0.0
	if (z <= -4.2e+131)
		tmp = t_1;
	elseif (z <= 4e+118)
		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[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]}, If[LessEqual[z, -4.2e+131], t$95$1, If[LessEqual[z, 4e+118], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999971e131 or 3.99999999999999987e118 < z

   1. Initial program 61.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 62.0

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

   3. Applied rewrites 62.0%

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

   4. Taylor expanded in z around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 63.1

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

   6. Applied rewrites 63.1%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-div N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lift--.f64 63.2

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

   9. Applied rewrites 63.2%

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

   if -4.19999999999999971e131 < z < 3.99999999999999987e118

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.0

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

   4. Applied rewrites 63.0%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 64.7

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

   6. Applied rewrites 64.7%

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

Alternative 11: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.75e+171) t (if (<= z 4.2e+118) (fma (- t x) (/ y a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.75e+171) {
		tmp = t;
	} else if (z <= 4.2e+118) {
		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 <= -3.75e+171)
		tmp = t;
	elseif (z <= 4.2e+118)
		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, -3.75e+171], t, If[LessEqual[z, 4.2e+118], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7499999999999999e171 or 4.2e118 < z

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 56.6%

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

   if -3.7499999999999999e171 < z < 4.2e118

   1. Initial program 88.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 61.1

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

   4. Applied rewrites 61.1%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 62.8

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

   6. Applied rewrites 62.8%

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

Alternative 12: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.75e+171) t (if (<= z 4e+118) (fma y (/ (- t x) a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.75e+171) {
		tmp = t;
	} else if (z <= 4e+118) {
		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 <= -3.75e+171)
		tmp = t;
	elseif (z <= 4e+118)
		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, -3.75e+171], t, If[LessEqual[z, 4e+118], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7499999999999999e171 or 3.99999999999999987e118 < z

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 56.6%

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

   if -3.7499999999999999e171 < z < 3.99999999999999987e118

   1. Initial program 88.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 61.1

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

   4. Applied rewrites 61.1%

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

Alternative 13: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+171) t (if (<= z 7.5e+116) (fma y (/ t a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+171) {
		tmp = t;
	} else if (z <= 7.5e+116) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+171)
		tmp = t;
	elseif (z <= 7.5e+116)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+171], t, If[LessEqual[z, 7.5e+116], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999995e171 or 7.5e116 < z

   1. Initial program 60.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 56.6%

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

   if -4.79999999999999995e171 < z < 7.5e116

   1. Initial program 88.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 61.2

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

   4. Applied rewrites 61.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 50.9%

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

Alternative 14: 38.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+160}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+160) t (if (<= z 7.5e+116) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+160) {
		tmp = t;
	} else if (z <= 7.5e+116) {
		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 <= (-3.5d+160)) then
        tmp = t
    else if (z <= 7.5d+116) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+160) {
		tmp = t;
	} else if (z <= 7.5e+116) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+160:
		tmp = t
	elif z <= 7.5e+116:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+160)
		tmp = t;
	elseif (z <= 7.5e+116)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+160)
		tmp = t;
	elseif (z <= 7.5e+116)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+160], t, If[LessEqual[z, 7.5e+116], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000026e160 or 7.5e116 < z

   1. Initial program 61.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 56.5%

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

   if -3.50000000000000026e160 < z < 7.5e116

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 31.2%

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

Alternative 15: 25.2% 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 81.0%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.2%

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

Reproduce

herbie shell --seed 2025093 
(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)))))