Average Error: 0.3 → 0.3
Time: 45.6s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]

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+0.3

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

  6. Applied add-cube-cbrt0.3

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

  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 2018360 
(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: 26.7s)Debug log

start625.0ms

Algorithm
intervals

setup341.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 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)))
0.0b
(- (+ (log (+ x y)) (log z)) t)

rewrite174.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

113.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
44.0ms
(- (+ (log (+ x y)) (log z)) t)
11.0ms
(+ (log (+ x y)) (log z))

series555.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

212.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
187.0ms
(- (+ (log (+ x y)) (log z)) t)
78.0ms
(* (- a 0.5) (log t))
78.0ms
(+ (log (+ x y)) (log z))

simplify4.8s

Counts
46 → 82
Calls

46 calls. Slowest were:

699.0ms
(* (+ (+ (log (+ x y)) (log z)) t) (+ (* a a) (+ (* 0.5 0.5) (* a 0.5))))
461.0ms
(- (* 2 (log -1)) (+ (log (/ -1 x)) (log (/ -1 z))))
392.0ms
(* (exp (- (+ (log (+ x y)) (log z)) t)) (exp (* (- a 0.5) (log t))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
3 → 58
Calls

3 calls. Slowest were:

26.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
14.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
4.0ms
(* (- a 0.5) (log t))

series385.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

191.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
117.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
76.0ms
(* (- a 0.5) (log t))

simplify5.1s

Counts
42 → 67
Calls

42 calls. Slowest were:

367.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
360.0ms
(* (+ x y) (exp (+ (- (log z) t) (* (- a 0.5) (log t)))))
342.0ms
(- (+ (* 0.5 (log (/ -1 t))) (+ (* a (log -1)) (* 0.5 (log -1)))) (+ t (+ (* a (log (/ -1 t))) (log (/ -1 z)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (log (sqrt (+ x y))) (log z))
0.3b
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
0.2b
(* (- a 0.5) (log t))
0.1b
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))

rewrite825.0ms

Algorithm
rewrite-expression-head
Counts
4 → 88
Calls

4 calls. Slowest were:

803.0ms
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
12.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
4.0ms
(+ (log (sqrt (+ x y))) (log z))

series530.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

328.0ms
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
73.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
73.0ms
(+ (log (sqrt (+ x y))) (log z))
56.0ms
(* (- a 0.5) (log t))

simplify3.5s

Counts
65 → 100
Calls

65 calls. Slowest were:

312.0ms
(* (- (* a a) (* 0.5 0.5)) (log t))
300.0ms
(* (+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (+ a 0.5))
298.0ms
(+ (* (- (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))))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ x y))
0.6b
(cbrt (+ x y))
0.6b
(cbrt (+ x y))
0.5b
(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
1.0ms
(cbrt (+ x y))
1.0ms
(cbrt (+ x y))

series669.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

209.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
164.0ms
(cbrt (+ x y))
153.0ms
(cbrt (+ x y))
143.0ms
(cbrt (+ x y))

simplify1.5s

Counts
59 → 87
Calls

59 calls. Slowest were:

214.0ms
(- (+ (* 2/3 (* x (pow (/ 1 y) 1/3))) (pow y 2/3)) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 4)) 1/3))))
162.0ms
(- (+ (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))))
148.0ms
(- (+ (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))))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms