Average Error: 0.2 → 0.3
Time: 55.3s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\sqrt[3]{\left(\left(\log \left(y + x\right) + \log z\right) \cdot \left(\log \left(y + x\right) + \log z\right)\right) \cdot \left(\log \left(y + x\right) + \log z\right)} - t\right) + \log t \cdot \left(a - 0.5\right)\]

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

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-cbrt-cube0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019005 
(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: 52.6s)Debug log

sample909.0ms

Algorithm
intervals

simplify342.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

341.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize52.0ms

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)

rewrite198.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

143.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
41.0ms
(- (+ (log (+ x y)) (log z)) t)
8.0ms
(* (- a 0.5) (log t))

series487.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

208.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
145.0ms
(- (+ (log (+ x y)) (log z)) t)
89.0ms
(+ (log (+ x y)) (log z))
46.0ms
(* (- a 0.5) (log t))

simplify3.4s

Counts
46 → 82
Calls

46 calls. Slowest were:

372.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
271.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))
242.0ms
(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Counts
4 → 90
Calls

4 calls. Slowest were:

24.0ms
(cbrt (* (* (+ (log (+ x y)) (log z)) (+ (log (+ x y)) (log z))) (+ (log (+ x y)) (log z))))
8.0ms
(+ (log (+ x y)) (log z))
7.0ms
(+ (log (+ x y)) (log z))

series266.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

70.0ms
(cbrt (* (* (+ (log (+ x y)) (log z)) (+ (log (+ x y)) (log z))) (+ (log (+ x y)) (log z))))
68.0ms
(+ (log (+ x y)) (log z))
66.0ms
(+ (log (+ x y)) (log z))
63.0ms
(+ (log (+ x y)) (log z))

simplify10.1s

Counts
64 → 102
Calls

64 calls. Slowest were:

806.0ms
(cbrt (* (* (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z))) (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))) (+ (pow (log (+ x y)) 3) (pow (log z) 3))))
724.0ms
(cbrt (* (* (+ (pow (log (+ x y)) 3) (pow (log z) 3)) (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))) (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))))
670.0ms
(cbrt (* (* (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z))) (+ (log (+ x y)) (log z))) (+ (log (+ x y)) (log z))))

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (log (+ x y)) 3)
0.7b
(pow (log z) 3)
0.5b
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
0.5b
(* (log z) (log z))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

5.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
4.0ms
(* (log z) (log z))
1.0ms
(pow (log (+ x y)) 3)

series885.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

304.0ms
(pow (log (+ x y)) 3)
218.0ms
(pow (log z) 3)
195.0ms
(- (* (log z) (log z)) (* (log (+ x y)) (log z)))
168.0ms
(* (log z) (log z))

simplify1.7s

Counts
46 → 85
Calls

46 calls. Slowest were:

375.0ms
(pow (- (log -1) (log (/ -1 x))) 3)
302.0ms
(pow (- (log -1) (log (/ -1 z))) 3)
296.0ms
(pow (- (log -1) (log (/ -1 z))) 2)

prune1.9s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
0.6b
(+ (log (+ x y)) (log z))
0.5b
(* (cbrt (- a 0.5)) (log t))
0.3b
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Counts
4 → 124
Calls

4 calls. Slowest were:

41.0ms
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))
11.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
9.0ms
(* (cbrt (- a 0.5)) (log t))

series368.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

112.0ms
(* (cbrt (- a 0.5)) (log t))
97.0ms
(+ (log (+ x y)) (log z))
87.0ms
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))
72.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))

simplify8.7s

Counts
121 → 136
Calls

121 calls. Slowest were:

656.0ms
(* (* (* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (cbrt (- a 0.5)))) (* (cbrt (- a 0.5)) (cbrt (- a 0.5)))) (* (- a 0.5) (* (* (log t) (log t)) (log t))))
446.0ms
(* (cbrt (- (* a a) (* 0.5 0.5))) (cbrt (- (pow a 3) (pow 0.5 3))))
445.0ms
(* (* (* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (cbrt (- a 0.5)))) (* (cbrt (- a 0.5)) (cbrt (- a 0.5)))) (* (* (* (cbrt (- a 0.5)) (log t)) (* (cbrt (- a 0.5)) (log t))) (* (cbrt (- a 0.5)) (log t))))

prune2.6s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.0b

regimes1.7s

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample15.7s

Algorithm
intervals