Average Error: 3.7 → 0
Time: 2.2s
Precision: binary64
\[-14 \leq a \land a \leq -13 \land -3 \leq b \land b \leq -2 \land 3 \leq c \land c \leq 3.5 \land 12.5 \leq d \land d \leq 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\sqrt[3]{1} \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\sqrt[3]{1} \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\right) \cdot 2
(FPCore (a b c d) :precision binary64 (* (+ a (+ b (+ c d))) 2.0))
↓
(FPCore (a b c d)
 :precision binary64
 (* (* (cbrt 1.0) (+ (+ a d) (+ b c))) 2.0))
double code(double a, double b, double c, double d) {
	return (a + (b + (c + d))) * 2.0;
}
↓
double code(double a, double b, double c, double d) {
	return (cbrt(1.0) * ((a + d) + (b + c))) * 2.0;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. Using strategy rm

  3. Applied associate-+r+_binary64_17312.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied add-cbrt-cube_binary64_18352.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]

  6. Simplified2.9

    \[\leadsto \sqrt[3]{\color{blue}{{\left(a + \left(d + \left(b + c\right)\right)\right)}^{3}}} \cdot 2\]
  7. Using strategy rm

  8. Applied associate-+r+_binary64_17310.6

    \[\leadsto \sqrt[3]{{\color{blue}{\left(\left(a + d\right) + \left(b + c\right)\right)}}^{3}} \cdot 2\]
  9. Using strategy rm

  10. Applied *-un-lft-identity_binary64_17990.6

    \[\leadsto \sqrt[3]{{\color{blue}{\left(1 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\right)}}^{3}} \cdot 2\]

  11. Applied unpow-prod-down_binary64_18780.6

    \[\leadsto \sqrt[3]{\color{blue}{{1}^{3} \cdot {\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}}} \cdot 2\]

  12. Applied cbrt-prod_binary64_18300.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}}\right)} \cdot 2\]

  13. Simplified0.6

    \[\leadsto \left(\color{blue}{\sqrt[3]{1}} \cdot \sqrt[3]{{\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}}\right) \cdot 2\]

  14. Simplified0

    \[\leadsto \left(\sqrt[3]{1} \cdot \color{blue}{\left(\left(a + d\right) + \left(b + c\right)\right)}\right) \cdot 2\]

  15. Final simplification0

    \[\leadsto \left(\sqrt[3]{1} \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020292 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))