Average Error: 0.2 → 0.3
Time: 50.3s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log z + \log \left(\sqrt{y + x}\right)\right)}^{3} + {\left(\log \left(\sqrt{y + x}\right)\right)}^{3}}{\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) \cdot \left(\log z + \log \left(\sqrt{y + x}\right)\right) - \log \left(\sqrt{y + x}\right) \cdot \left(\log z + \log \left(\sqrt{y + x}\right)\right)\right) + \log \left(\sqrt{y + x}\right) \cdot \log \left(\sqrt{y + x}\right)} - t\right) + \log t \cdot \left(a - 0.5\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

    \[\leadsto \left(\left(\log \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{x + y}\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Applied log-prod0.2

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt{x + y}\right) + \log \left(\sqrt{x + y}\right)\right)} + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Applied associate-+l+0.3

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \log z\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
  6. Using strategy rm

  7. Applied flip3-+0.3

    \[\leadsto \left(\color{blue}{\frac{{\left(\log \left(\sqrt{x + y}\right)\right)}^{3} + {\left(\log \left(\sqrt{x + y}\right) + \log z\right)}^{3}}{\log \left(\sqrt{x + y}\right) \cdot \log \left(\sqrt{x + y}\right) + \left(\left(\log \left(\sqrt{x + y}\right) + \log z\right) \cdot \left(\log \left(\sqrt{x + y}\right) + \log z\right) - \log \left(\sqrt{x + y}\right) \cdot \left(\log \left(\sqrt{x + y}\right) + \log z\right)\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  8. Final simplification0.3

    \[\leadsto \left(\frac{{\left(\log z + \log \left(\sqrt{y + x}\right)\right)}^{3} + {\left(\log \left(\sqrt{y + x}\right)\right)}^{3}}{\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) \cdot \left(\log z + \log \left(\sqrt{y + x}\right)\right) - \log \left(\sqrt{y + x}\right) \cdot \left(\log z + \log \left(\sqrt{y + x}\right)\right)\right) + \log \left(\sqrt{y + x}\right) \cdot \log \left(\sqrt{y + x}\right)} - t\right) + \log t \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019007 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))

Details

Time bar (total: 48.0s)Debug log

sample353.0ms

Algorithm
intervals

simplify214.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

214.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (log (+ x y)) (log z))
0.1b
(* (- a 0.5) (log t))
0.1b
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.0b
(- (+ (log (+ x y)) (log z)) t)

rewrite110.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

75.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
22.0ms
(- (+ (log (+ x y)) (log z)) t)
8.0ms
(* (- a 0.5) (log t))

series435.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

203.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
130.0ms
(- (+ (log (+ x y)) (log z)) t)
58.0ms
(+ (log (+ x y)) (log z))
44.0ms
(* (- a 0.5) (log t))

simplify3.0s

Counts
46 → 82
Calls

46 calls. Slowest were:

306.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
210.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))
208.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (log (sqrt (+ x y))) (log z))
0.4b
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
0.1b
(* (- a 0.5) (log t))
0.1b
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))

rewrite375.0ms

Algorithm
rewrite-expression-head
Counts
4 → 88
Calls

4 calls. Slowest were:

332.0ms
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
26.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
9.0ms
(+ (log (sqrt (+ x y))) (log z))

series514.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

292.0ms
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
88.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
81.0ms
(+ (log (sqrt (+ x y))) (log z))
52.0ms
(* (- a 0.5) (log t))

simplify3.0s

Counts
65 → 100
Calls

65 calls. Slowest were:

279.0ms
(+ (* (- (pow (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) 3) (pow t 3)) (+ (* a a) (+ (* 0.5 0.5) (* a 0.5)))) (* (+ (* (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))) (+ (* t t) (* (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))) (* (- (pow a 3) (pow 0.5 3)) (log t))))
279.0ms
(* (+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (+ a 0.5))
215.0ms
(+ (* (- (* (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))) (* t t)) (+ a 0.5)) (* (+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- (* a a) (* 0.5 0.5)) (log t))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (log (sqrt (+ x y))) 3)
0.7b
(pow (+ (log (sqrt (+ x y))) (log z)) 3)
0.5b
(* (log (sqrt (+ x y))) (log (sqrt (+ x y))))
0.5b
(- (* (+ (log (sqrt (+ x y))) (log z)) (+ (log (sqrt (+ x y))) (log z))) (* (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Counts
4 → 121
Calls

4 calls. Slowest were:

31.0ms
(- (* (+ (log (sqrt (+ x y))) (log z)) (+ (log (sqrt (+ x y))) (log z))) (* (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))))
12.0ms
(pow (+ (log (sqrt (+ x y))) (log z)) 3)
11.0ms
(* (log (sqrt (+ x y))) (log (sqrt (+ x y))))

series969.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

508.0ms
(pow (+ (log (sqrt (+ x y))) (log z)) 3)
205.0ms
(pow (log (sqrt (+ x y))) 3)
162.0ms
(- (* (+ (log (sqrt (+ x y))) (log z)) (+ (log (sqrt (+ x y))) (log z))) (* (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))))
94.0ms
(* (log (sqrt (+ x y))) (log (sqrt (+ x y))))

simplify10.1s

Counts
112 → 133
Calls

112 calls. Slowest were:

682.0ms
(* (* (+ (* (log (sqrt (+ x y))) (log (sqrt (+ x y)))) (- (* (log z) (log z)) (* (log (sqrt (+ x y))) (log z)))) (+ (* (log (sqrt (+ x y))) (log (sqrt (+ x y)))) (- (* (log z) (log z)) (* (log (sqrt (+ x y))) (log z))))) (- (log (sqrt (+ x y))) (log z)))
620.0ms
(* (* (+ (* (log (sqrt (+ x y))) (log (sqrt (+ x y)))) (- (* (log z) (log z)) (* (log (sqrt (+ x y))) (log z)))) (- (log (sqrt (+ x y))) (log z))) (- (log (sqrt (+ x y))) (log z)))
423.0ms
(* (+ (* (log (sqrt (+ x y))) (log (sqrt (+ x y)))) (- (* (log z) (log z)) (* (log (sqrt (+ x y))) (log z)))) (- (log (sqrt (+ x y))) (log z)))

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
0.4b
(+ (log (sqrt (+ x y))) (log z))
0.4b
(* (cbrt (- a 0.5)) (log t))
0.4b
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 108
Calls

4 calls. Slowest were:

25.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
11.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
9.0ms
(+ (log (sqrt (+ x y))) (log z))

series334.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

134.0ms
(* (cbrt (- a 0.5)) (log t))
74.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
71.0ms
(+ (log (sqrt (+ x y))) (log z))
54.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))

simplify2.7s

Counts
87 → 120
Calls

87 calls. Slowest were:

326.0ms
(- (* (pow (pow a 2) 1/3) (pow (cbrt -1) 2)) (+ (* 0.027777777777777776 (* (pow (/ 1 (pow a 4)) 1/3) (pow (cbrt -1) 2))) (* 0.3333333333333333 (* (pow (/ 1 a) 1/3) (pow (cbrt -1) 2)))))
316.0ms
(- (+ (* (log t) (pow -0.5 1/3)) (* 0.2222222222222222 (* (* (pow a 2) (log t)) (pow -0.5 1/3)))) (+ (* 0.6666666666666666 (* (* a (log t)) (pow -0.5 1/3))) (* 1/6 (* (* (pow a 2) (log t)) (pow -32.0 1/3)))))
316.0ms
(- (+ (* 2.2222222222222223 (* (pow a 2) (pow 0.25 1/3))) (pow 0.25 1/3)) (+ (* 0.16666666666666666 (* (pow a 2) (pow (/ 1 (pow 0.25 5)) 1/3))) (* 1.3333333333333333 (* a (pow 0.25 1/3)))))

prune2.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes1.7s

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch6.0ms

end0.0ms

sample15.2s

Algorithm
intervals