Average Error: 0.2 → 0.3
Time: 39.6s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(y + x\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\left(\sqrt[3]{{\left(\log z\right)}^{6}} - \log \left(y + x\right) \cdot \log z\right) + \log \left(y + x\right) \cdot \log \left(y + x\right)} - t\right) + \log t \cdot \left(a - 0.5\right)\]

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

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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 flip3-+0.3

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

  5. Applied add-cbrt-cube0.3

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

  6. Applied add-cbrt-cube0.4

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

  7. Applied cbrt-unprod0.3

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

  8. Simplified0.3

    \[\leadsto \left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log \left(x + y\right) \cdot \log \left(x + y\right) + \left(\sqrt[3]{\color{blue}{{\left(\log z\right)}^{6}}} - \log \left(x + y\right) \cdot \log z\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  9. Final simplification0.3

    \[\leadsto \left(\frac{{\left(\log \left(y + x\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\left(\sqrt[3]{{\left(\log z\right)}^{6}} - \log \left(y + x\right) \cdot \log z\right) + \log \left(y + x\right) \cdot \log \left(y + x\right)} - t\right) + \log t \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(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: 37.4s)Debug log

sample489.0ms

Algorithm
intervals

simplify317.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

317.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ (log (+ x y)) (log z))
0.2b
(* (- a 0.5) (log t))
0.1b
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Counts
3 → 69
Calls

3 calls. Slowest were:

122.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
5.0ms
(+ (log (+ x y)) (log z))
4.0ms
(* (- a 0.5) (log t))

series290.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

165.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
78.0ms
(+ (log (+ x y)) (log z))
47.0ms
(* (- a 0.5) (log t))

simplify3.6s

Counts
44 → 78
Calls

44 calls. Slowest were:

447.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
291.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))
248.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (log z) 3)
0.7b
(pow (log (+ x y)) 3)
0.6b
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
0.6b
(* (log z) (log z))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 83
Calls

4 calls. Slowest were:

11.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
6.0ms
(* (log z) (log z))
2.0ms
(pow (log (+ x y)) 3)

series882.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

285.0ms
(pow (log (+ x y)) 3)
203.0ms
(* (log z) (log z))
197.0ms
(pow (log z) 3)
197.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))

simplify2.5s

Counts
49 → 95
Calls

49 calls. Slowest were:

653.0ms
(pow (- (log -1) (log (/ -1 z))) 2)
553.0ms
(pow (- (log -1) (log (/ -1 z))) 3)
467.0ms
(pow (- (log -1) (log (/ -1 x))) 3)

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

1.2b
(pow (log z) 6)
0.7b
(pow (log z) 3)
0.7b
(pow (log (+ x y)) 3)
0.6b
(- (cbrt (pow (log z) 6)) (* (log (+ x y)) (log z)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 91
Calls

4 calls. Slowest were:

19.0ms
(- (cbrt (pow (log z) 6)) (* (log (+ x y)) (log z)))
3.0ms
(pow (log (+ x y)) 3)
2.0ms
(pow (log z) 6)

series992.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

308.0ms
(pow (log (+ x y)) 3)
245.0ms
(pow (log z) 3)
222.0ms
(pow (log z) 6)
216.0ms
(- (cbrt (pow (log z) 6)) (* (log (+ x y)) (log z)))

simplify2.2s

Counts
64 → 103
Calls

64 calls. Slowest were:

519.0ms
(pow (- (log -1) (log (/ -1 z))) 3)
516.0ms
(pow (- (log -1) (log (/ -1 x))) 3)
162.0ms
(- (+ (pow (log (/ -1 z)) 2) (* (log (/ -1 x)) (log -1))) (+ (* (log (/ -1 z)) (log -1)) (* (log (/ -1 x)) (log (/ -1 z)))))

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (log (+ x y)) (log z))
0.5b
(cbrt (log t))
0.5b
(cbrt (log t))
0.5b
(cbrt (log t))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 63
Calls

4 calls. Slowest were:

10.0ms
(+ (log (+ x y)) (log z))
1.0ms
(cbrt (log t))
1.0ms
(cbrt (log t))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

433.0ms
(cbrt (log t))
359.0ms
(cbrt (log t))
321.0ms
(cbrt (log t))
90.0ms
(+ (log (+ x y)) (log z))

simplify574.0ms

Counts
31 → 75
Calls

31 calls. Slowest were:

310.0ms
(- (* 2 (log -1)) (+ (log (/ -1 x)) (log (/ -1 z))))
47.0ms
(pow (- (log -1) (log (/ -1 t))) 1/3)
41.0ms
(- (+ (log (/ 1 z)) (log (/ 1 x))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes1.9s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample15.1s

Algorithm
intervals