Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Percentage Accurate: 87.8% → 99.9%

Time: 3.7s

Alternatives: 8

Speedup: 1.0×

• 79.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (+ x (* y (- z x))) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x + (y * (z - x))) / z
END code

Initial Program: 87.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (+ x (* y (- z x))) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x + (y * (z - x))) / z
END code

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma (- 1.0 y) (/ x z) y))

C

double code(double x, double y, double z) {
	return fma((1.0 - y), (x / z), y);
}

Julia

function code(x, y, z)
	return fma(Float64(1.0 - y), Float64(x / z), y)
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - y), $MachinePrecision] * N[(x / z), $MachinePrecision] + y), $MachinePrecision]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(((1) - y) * (x / z)) + y
END code

Derivation

1. Initial program 87.8%

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

3. Applied rewrites 87.6%

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

5. Applied rewrites 99.9%

   \[\leadsto \mathsf{fma}\left(1 - y, \frac{x}{z}, y\right) \]
6. Add Preprocessing

Alternative 2: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := y \cdot \frac{z - x}{z}\\ \mathbf{if}\;y \leq -83405507.39250578:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 254.09303055021542:\\ \;\;\;\;\frac{\mathsf{fma}\left(z - x, y, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* y (/ (- z x) z))))
  (if (<= y -83405507.39250578)
    t_0
    (if (<= y 254.09303055021542) (/ (fma (- z x) y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * ((z - x) / z);
	double tmp;
	if (y <= -83405507.39250578) {
		tmp = t_0;
	} else if (y <= 254.09303055021542) {
		tmp = fma((z - x), y, x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(z - x) / z))
	tmp = 0.0
	if (y <= -83405507.39250578)
		tmp = t_0;
	elseif (y <= 254.09303055021542)
		tmp = Float64(fma(Float64(z - x), y, x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -83405507.39250578], t$95$0, If[LessEqual[y, 254.09303055021542], N[(N[(N[(z - x), $MachinePrecision] * y + x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (y * ((z - x) / z)) IN
		LET tmp_1 = IF (y <= (254093030550215416951687075197696685791015625e-42)) THEN ((((z - x) * y) + x) / z) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-8340550739250577986240386962890625e-26)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -83405507.39250578 or 254.09303055021542 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 53.6%

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

   6. Applied rewrites 67.6%

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

   if -83405507.39250578 < y < 254.09303055021542

   1. Initial program 87.8%

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

   3. Applied rewrites 87.8%

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

Alternative 3: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := y \cdot \frac{z - x}{z}\\ \mathbf{if}\;y \leq -2509.0653284185646:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3925.6693208389647:\\ \;\;\;\;\mathsf{fma}\left(y, 1, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* y (/ (- z x) z))))
  (if (<= y -2509.0653284185646)
    t_0
    (if (<= y 3925.6693208389647) (fma y 1.0 (/ x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * ((z - x) / z);
	double tmp;
	if (y <= -2509.0653284185646) {
		tmp = t_0;
	} else if (y <= 3925.6693208389647) {
		tmp = fma(y, 1.0, (x / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(z - x) / z))
	tmp = 0.0
	if (y <= -2509.0653284185646)
		tmp = t_0;
	elseif (y <= 3925.6693208389647)
		tmp = fma(y, 1.0, Float64(x / z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2509.0653284185646], t$95$0, If[LessEqual[y, 3925.6693208389647], N[(y * 1.0 + N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (y * ((z - x) / z)) IN
		LET tmp_1 = IF (y <= (392566932083896472249762155115604400634765625e-41)) THEN ((y * (1)) + (x / z)) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-250906532841856460436247289180755615234375e-38)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2509.0653284185646 or 3925.6693208389647 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 53.6%

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

   6. Applied rewrites 67.6%

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

   if -2509.0653284185646 < y < 3925.6693208389647

   1. Initial program 87.8%

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

   3. Applied rewrites 93.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 78.2%

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

Alternative 4: 95.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma x (/ (- 1.0 y) z) y))

C

double code(double x, double y, double z) {
	return fma(x, ((1.0 - y) / z), y);
}

Julia

function code(x, y, z)
	return fma(x, Float64(Float64(1.0 - y) / z), y)
end

Wolfram

code[x_, y_, z_] := N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision] + y), $MachinePrecision]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (((1) - y) / z)) + y
END code

Derivation

1. Initial program 87.8%

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

3. Applied rewrites 87.6%

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

5. Applied rewrites 99.9%

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

7. Applied rewrites 95.5%

   \[\leadsto \mathsf{fma}\left(x, \frac{1 - y}{z}, y\right) \]
8. Add Preprocessing

Alternative 5: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 2.5235973101497354 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y 2.5235973101497354e+178) (fma y 1.0 (/ x z)) (* z (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5235973101497354e+178) {
		tmp = fma(y, 1.0, (x / z));
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5235973101497354e+178)
		tmp = fma(y, 1.0, Float64(x / z));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5235973101497354e+178], N[(y * 1.0 + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (y <= (25235973101497354482214954917900760340524771587181319724948153287136140190976829088846080717156719018215736973452903454574359277303968890614466637516791816677995228882765573259264)) THEN ((y * (1)) + (x / z)) ELSE (z * (y / z)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < 2.5235973101497354e178

   1. Initial program 87.8%

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

   3. Applied rewrites 93.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 78.2%

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

   if 2.5235973101497354e178 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 53.6%

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

   6. Applied rewrites 55.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 36.9%

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

Alternative 6: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.3808892104572836:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.71392951001371 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (/ y z))))
  (if (<= y -1.3808892104572836)
    t_0
    (if (<= y 5.71392951001371e-24) (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.3808892104572836) {
		tmp = t_0;
	} else if (y <= 5.71392951001371e-24) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y / z)
    if (y <= (-1.3808892104572836d0)) then
        tmp = t_0
    else if (y <= 5.71392951001371d-24) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.3808892104572836) {
		tmp = t_0;
	} else if (y <= 5.71392951001371e-24) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -1.3808892104572836:
		tmp = t_0
	elif y <= 5.71392951001371e-24:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -1.3808892104572836)
		tmp = t_0;
	elseif (y <= 5.71392951001371e-24)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -1.3808892104572836)
		tmp = t_0;
	elseif (y <= 5.71392951001371e-24)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3808892104572836], t$95$0, If[LessEqual[y, 5.71392951001371e-24], N[(x / z), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (z * (y / z)) IN
		LET tmp_1 = IF (y <= (5713929510013710309954588345103281388526423837570695643911942366958978123392398629221133887767791748046875e-129)) THEN (x / z) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-13808892104572836334597241148003377020359039306640625e-52)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.3808892104572836 or 5.7139295100137103e-24 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 53.6%

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

   6. Applied rewrites 55.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 36.9%

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

   if -1.3808892104572836 < y < 5.7139295100137103e-24

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 39.8%

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

Alternative 7: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -4.396452877645846 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.71392951001371 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -4.396452877645846e-84)
  y
  (if (<= y 5.71392951001371e-24) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.396452877645846e-84) {
		tmp = y;
	} else if (y <= 5.71392951001371e-24) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.396452877645846d-84)) then
        tmp = y
    else if (y <= 5.71392951001371d-24) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.396452877645846e-84) {
		tmp = y;
	} else if (y <= 5.71392951001371e-24) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.396452877645846e-84:
		tmp = y
	elif y <= 5.71392951001371e-24:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.396452877645846e-84)
		tmp = y;
	elseif (y <= 5.71392951001371e-24)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.396452877645846e-84)
		tmp = y;
	elseif (y <= 5.71392951001371e-24)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.396452877645846e-84], y, If[LessEqual[y, 5.71392951001371e-24], N[(x / z), $MachinePrecision], y]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp_1 = IF (y <= (5713929510013710309954588345103281388526423837570695643911942366958978123392398629221133887767791748046875e-129)) THEN (x / z) ELSE y ENDIF IN
	LET tmp = IF (y <= (-43964528776458464081694827798763004894182085276933175051225769637393906829390866746776185321362175168060435304308169415223731245090346098651524509615456527276516670822493343078795340840138714666963115911164916571607363948714919388294219970703125e-328)) THEN y ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -4.3964528776458464e-84 or 5.7139295100137103e-24 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto y \]
   3. Step-by-step derivation

   4. Applied rewrites 40.8%

      \[\leadsto y \]

   if -4.3964528776458464e-84 < y < 5.7139295100137103e-24

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 39.8%

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

Alternative 8: 40.8% accurate, 13.0× speedup

Math

\[y \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  y)

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	y
END code

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in x around 0

   \[\leadsto y \]
3. Step-by-step derivation

4. Applied rewrites 40.8%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (/ (+ x (* y (- z x))) z))