Average Error: 0.2 → 0.3
Time: 45.1s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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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-cube-cbrt0.2

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2018365 
(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: 25.1s)Debug log

start442.0ms

Algorithm
intervals

setup301.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (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)

rewrite109.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

79.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
22.0ms
(- (+ (log (+ x y)) (log z)) t)
4.0ms
(+ (log (+ x y)) (log z))

series435.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

177.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
154.0ms
(- (+ (log (+ x y)) (log z)) t)
57.0ms
(+ (log (+ x y)) (log z))
47.0ms
(* (- a 0.5) (log t))

simplify3.9s

Counts
46 → 82
Calls

46 calls. Slowest were:

551.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))
470.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
322.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

7.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
1.0ms
(cbrt (+ x y))
0.0ms
(cbrt (+ x y))

series642.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

205.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
153.0ms
(cbrt (+ x y))
148.0ms
(cbrt (+ x y))
136.0ms
(cbrt (+ x y))

simplify1.6s

Counts
59 → 87
Calls

59 calls. Slowest were:

182.0ms
(- (+ (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))))
178.0ms
(- (+ (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))))
170.0ms
(- (+ (* 2/3 (* x (pow (/ 1 y) 1/3))) (pow y 2/3)) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 4)) 1/3))))

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b
(pow (+ x y) 2/3)
0.5b
(cbrt (+ x y))
0.5b
(+ (log (pow (+ x y) 2/3)) (+ (log (cbrt (+ x y))) (log z)))
0.4b
(+ (log (cbrt (+ x y))) (log z))

rewrite41.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

23.0ms
(+ (log (pow (+ x y) 2/3)) (+ (log (cbrt (+ x y))) (log z)))
13.0ms
(+ (log (cbrt (+ x y))) (log z))
2.0ms
(pow (+ x y) 2/3)

series606.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

178.0ms
(+ (log (pow (+ x y) 2/3)) (+ (log (cbrt (+ x y))) (log z)))
157.0ms
(cbrt (+ x y))
140.0ms
(pow (+ x y) 2/3)
131.0ms
(+ (log (cbrt (+ x y))) (log z))

simplify2.4s

Counts
47 → 83
Calls

47 calls. Slowest were:

713.0ms
(- (+ (log (* (pow (* x -1) 1/3) (cbrt -1))) (log -1)) (log (/ -1 z)))
274.0ms
(+ (log (pow y 1/3)) (+ (log (pow y 2/3)) (log z)))
267.0ms
(- (+ (log (pow (/ 1 x) -1/3)) (log (pow (/ 1 x) -2/3))) (log (/ 1 z)))

prune1.9s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (- (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)

rewrite79.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

47.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
25.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
4.0ms
(* (- a 0.5) (log t))

series508.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

247.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))
115.0ms
(+ (- (log z) t) (* (- a 0.5) (log t)))
91.0ms
(- (log z) t)
54.0ms
(* (- a 0.5) (log t))

simplify5.7s

Counts
45 → 81
Calls

45 calls. Slowest were:

447.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
438.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (* a (log (/ 1 t))))))
436.0ms
(+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes1.9s

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms