Average Error: 0.3 → 0.3
Time: 56.8s
Precision: 64
Internal Precision: 128
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(a - 0.5\right) \cdot \log t + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2018362 
(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: 36.2s)Debug log

start463.0ms

Algorithm
intervals

setup583.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log (+ y x)) (* (- a 0.5) (log t)))
0.2b
(* (- a 0.5) (log t))
0.2b
(- (+ (log (+ y x)) (* (- a 0.5) (log t))) (- t (log z)))
0.0b
(- t (log z))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

19.0ms
(- (+ (log (+ y x)) (* (- a 0.5) (log t))) (- t (log z)))
8.0ms
(* (- a 0.5) (log t))
5.0ms
(+ (log (+ y x)) (* (- a 0.5) (log t)))

series306.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

120.0ms
(- (+ (log (+ y x)) (* (- a 0.5) (log t))) (- t (log z)))
114.0ms
(+ (log (+ y x)) (* (- a 0.5) (log t)))
46.0ms
(* (- a 0.5) (log t))
25.0ms
(- t (log z))

simplify4.4s

Counts
47 → 83
Calls

47 calls. Slowest were:

398.0ms
(* (- (log (+ y x)) (* (- a 0.5) (log t))) (+ t (log z)))
348.0ms
(- (+ (* a (log t)) (+ (log z) (log x))) (+ t (* 0.5 (log t))))
288.0ms
(- (+ (log (+ y x)) (* (- a 0.5) (log t))) (- t (log z)))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (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)

rewrite182.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

126.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
44.0ms
(- (+ (log (+ x y)) (log z)) t)
6.0ms
(+ (log (+ x y)) (log z))

series486.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

200.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
164.0ms
(- (+ (log (+ x y)) (log z)) t)
62.0ms
(* (- a 0.5) (log t))
60.0ms
(+ (log (+ x y)) (log z))

simplify3.7s

Counts
46 → 82
Calls

46 calls. Slowest were:

444.0ms
(- (+ (* a (log t)) (+ (log z) (log y))) (+ t (* 0.5 (log t))))
287.0ms
(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))
246.0ms
(- (* 2 (log -1)) (+ (log (/ -1 x)) (log (/ -1 z))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
0.4b
(* (cbrt (- a 0.5)) (log t))
0.4b
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))
0.3b
(cbrt (- a 0.5))

rewrite44.0ms

Algorithm
rewrite-expression-head
Counts
4 → 119
Calls

4 calls. Slowest were:

21.0ms
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))
10.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
9.0ms
(* (cbrt (- a 0.5)) (log t))

series367.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

140.0ms
(* (cbrt (- a 0.5)) (log t))
104.0ms
(* (* (cbrt (- a 0.5)) (cbrt (- a 0.5))) (* (cbrt (- a 0.5)) (log t)))
78.0ms
(* (cbrt (- a 0.5)) (cbrt (- a 0.5)))
45.0ms
(cbrt (- a 0.5))

simplify8.7s

Counts
118 → 131
Calls

118 calls. Slowest were:

607.0ms
(* (* (* (* (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))))
492.0ms
(* (* (* (* (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))))
331.0ms
(- (+ (* 2.2222222222222223 (* (pow a 2) (pow 0.25 1/3))) (pow 0.25 1/3)) (+ (* 0.16666666666666666 (* (pow a 2) (pow (/ 1 (pow 0.25 5)) 1/3))) (* 1.3333333333333333 (* a (pow 0.25 1/3)))))

prune3.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

20.0ms
(* (cbrt (* (- a 0.5) (log t))) (cbrt (* (- a 0.5) (log t))))
4.0ms
(cbrt (* (- a 0.5) (log t)))
4.0ms
(cbrt (* (- a 0.5) (log t)))

series433.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

135.0ms
(* (cbrt (* (- a 0.5) (log t))) (cbrt (* (- a 0.5) (log t))))
118.0ms
(cbrt (* (- a 0.5) (log t)))
93.0ms
(cbrt (* (- a 0.5) (log t)))
88.0ms
(cbrt (* (- a 0.5) (log t)))

simplify6.5s

Counts
49 → 77
Calls

49 calls. Slowest were:

503.0ms
(- (exp (* 1/3 (- (log (- (log (/ 1 t)))) (log (/ 1 a))))) (+ (* 0.16666666666666666 (/ (exp (* 1/3 (- (log (- (log (/ 1 t)))) (log (/ 1 a))))) a)) (* 0.027777777777777776 (/ (exp (* 1/3 (- (log (- (log (/ 1 t)))) (log (/ 1 a))))) (pow a 2)))))
406.0ms
(* (* (- a 0.5) (log t)) (* (- a 0.5) (log t)))
404.0ms
(- (exp (* 1/3 (- (log (pow (log (/ 1 t)) 2)) (* 2 (log (/ 1 a)))))) (+ (* 0.027777777777777776 (/ (exp (* 1/3 (- (log (pow (log (/ 1 t)) 2)) (* 2 (log (/ 1 a)))))) (pow a 2))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log (pow (log (/ 1 t)) 2)) (* 2 (log (/ 1 a)))))) a))))

prune1.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.0b

regimes2.4s

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms