Average Error: 0.2 → 0.3
Time: 35.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(y + x\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\left(\log z \cdot \log z - \log \left(y + x\right) \cdot \log z\right) + \log \left(y + x\right) \cdot \log \left(y + x\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

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 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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019002 
(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: 33.2s)Debug log

sample492.0ms

Algorithm
intervals

simplify332.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

332.0ms
(+ (- (+ (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: 0.3b

localize29.0ms

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)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Counts
3 → 56
Calls

3 calls. Slowest were:

78.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
4.0ms
(+ (log (+ x y)) (log z))
4.0ms
(* (- a 0.5) (log t))

series318.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

186.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
70.0ms
(+ (log (+ x y)) (log z))
62.0ms
(* (- a 0.5) (log t))

simplify2.9s

Counts
40 → 65
Calls

40 calls. Slowest were:

353.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
294.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))
235.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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 → 73
Calls

4 calls. Slowest were:

10.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
7.0ms
(* (log z) (log z))
2.0ms
(pow (log (+ x y)) 3)

series940.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

285.0ms
(pow (log (+ x y)) 3)
260.0ms
(pow (log z) 3)
202.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
192.0ms
(* (log z) (log z))

simplify1.6s

Counts
46 → 85
Calls

46 calls. Slowest were:

370.0ms
(pow (- (log -1) (log (/ -1 x))) 3)
318.0ms
(pow (- (log -1) (log (/ -1 z))) 3)
255.0ms
(pow (- (log -1) (log (/ -1 z))) 2)

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))
0.6b
(- (log (+ x y)) (log z))
0.6b
(* (log z) (log z))
0.5b
(* (log (+ x y)) (log (+ x y)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

12.0ms
(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))
10.0ms
(* (log (+ x y)) (log (+ x y)))
9.0ms
(- (log (+ x y)) (log z))

series563.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

176.0ms
(* (log z) (log z))
166.0ms
(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))
130.0ms
(* (log (+ x y)) (log (+ x y)))
91.0ms
(- (log (+ x y)) (log z))

simplify1.4s

Counts
60 → 99
Calls

60 calls. Slowest were:

340.0ms
(pow (- (log -1) (log (/ -1 z))) 2)
317.0ms
(pow (- (log -1) (log (/ -1 x))) 2)
163.0ms
(- (pow (log (/ 1 x)) 2) (pow (log (/ 1 z)) 2))

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 51
Calls

4 calls. Slowest were:

9.0ms
(+ (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:

394.0ms
(cbrt (log t))
370.0ms
(cbrt (log t))
347.0ms
(cbrt (log t))
79.0ms
(+ (log (+ x y)) (log z))

simplify487.0ms

Counts
29 → 63
Calls

29 calls. Slowest were:

253.0ms
(- (* 2 (log -1)) (+ (log (/ -1 x)) (log (/ -1 z))))
52.0ms
(log (- (* x x) (* y y)))
50.0ms
(pow (- (log -1) (log (/ -1 t))) 1/3)

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes2.0s

Accuracy

0% (0.2b remaining)

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

bsearch6.0ms

end0.0ms

sample14.7s

Algorithm
intervals