Average Error: 0.3 → 0.3
Time: 43.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]

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 0.3

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

  3. Applied associate--l+0.3

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

  4. Applied associate-+l+0.2

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

  6. Applied add-cube-cbrt0.2

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019008 
(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: 41.6s)Debug log

sample408.0ms

Algorithm
intervals

simplify550.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

550.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (log (+ x y)) (log z))
0.1b
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b
(* (- a 0.5) (log t))
0.0b
(- (+ (log (+ x y)) (log z)) t)

rewrite163.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

103.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
46.0ms
(- (+ (log (+ x y)) (log z)) t)
8.0ms
(* (- a 0.5) (log t))

series607.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

252.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
189.0ms
(- (+ (log (+ x y)) (log z)) t)
99.0ms
(+ (log (+ x y)) (log z))
66.0ms
(* (- a 0.5) (log t))

simplify3.5s

Counts
46 → 82
Calls

46 calls. Slowest were:

465.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
276.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))
242.0ms
(* (* (* (- a 0.5) (- a 0.5)) (- a 0.5)) (* (* (log t) (log t)) (log t)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

33.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
17.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
8.0ms
(* (- a 0.5) (log t))

series483.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

246.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
98.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
78.0ms
(- (log z) t)
60.0ms
(* (- a 0.5) (log t))

simplify5.3s

Counts
45 → 81
Calls

45 calls. Slowest were:

483.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
386.0ms
(- (+ (* 0.5 (log (/ -1 t))) (+ (* a (log -1)) (* 0.5 (log -1)))) (+ t (+ (* a (log (/ -1 t))) (log (/ -1 z)))))
378.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x y))
0.5b
(cbrt (+ x y))
0.5b
(cbrt (+ x y))
0.5b
(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
1.0ms
(cbrt (+ x y))
1.0ms
(cbrt (+ x y))

series638.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

225.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
149.0ms
(cbrt (+ x y))
136.0ms
(cbrt (+ x y))
129.0ms
(cbrt (+ x y))

simplify1.6s

Counts
59 → 87
Calls

59 calls. Slowest were:

204.0ms
(- (+ (* 2/3 (* x (pow (/ 1 y) 1/3))) (pow y 2/3)) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 4)) 1/3))))
186.0ms
(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))
169.0ms
(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (- a 0.5) (log t))) (cbrt (* (- a 0.5) (log t))))
0.5b
(cbrt (* (- a 0.5) (log t)))
0.5b
(cbrt (* (- a 0.5) (log t)))
0.5b
(cbrt (* (- a 0.5) (log t)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

12.0ms
(* (cbrt (* (- a 0.5) (log t))) (cbrt (* (- a 0.5) (log t))))
5.0ms
(cbrt (* (- a 0.5) (log t)))
2.0ms
(cbrt (* (- a 0.5) (log t)))

series464.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

130.0ms
(* (cbrt (* (- a 0.5) (log t))) (cbrt (* (- a 0.5) (log t))))
120.0ms
(cbrt (* (- a 0.5) (log t)))
119.0ms
(cbrt (* (- a 0.5) (log t)))
94.0ms
(cbrt (* (- a 0.5) (log t)))

simplify5.7s

Counts
49 → 77
Calls

49 calls. Slowest were:

386.0ms
(- (pow (* -0.5 (log t)) 1/3) (+ (* 0.4444444444444444 (* (pow a 2) (pow (* (log t) -0.5) 1/3))) (* 0.6666666666666666 (* a (pow (* (log t) -0.5) 1/3)))))
372.0ms
(* (* (- a 0.5) (log t)) (* (- a 0.5) (log t)))
354.0ms
(- (pow (* 0.25 (pow (log t) 2)) 1/3) (+ (* 1.3333333333333333 (* a (pow (* 0.25 (pow (log t) 2)) 1/3))) (* 0.4444444444444442 (* (pow a 2) (pow (* 0.25 (pow (log t) 2)) 1/3)))))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes1.4s

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample14.5s

Algorithm
intervals