Average Error: 2.0 → 2.0
Time: 51.4s
Precision: 64
Internal Precision: 128
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

  2. Taylor expanded around 0 2.0

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(t \cdot \log a - 1.0 \cdot \log a\right)}\right) - b}}{y}\]

  3. Simplified2.0

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(t - 1.0\right) \cdot \log a}\right) - b}}{y}\]

  4. Final simplification2.0

    \[\leadsto \frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}\]

Reproduce

herbie shell --seed 2019002 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

Details

Time bar (total: 50.2s)Debug log

sample743.0ms

Algorithm
intervals

simplify382.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

382.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.9b
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.6b
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.3b
(* y (log z))
0.1b
(* (- t 1.0) (log a))

rewrite43.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

26.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
4.0ms
(* (- t 1.0) (log a))

series488.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

221.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
166.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
63.0ms
(* (- t 1.0) (log a))
38.0ms
(* y (log z))

simplify3.1s

Counts
34 → 69
Calls

34 calls. Slowest were:

420.0ms
(* -1 (* (log (/ 1 z)) y))
340.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
224.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

Local error

Found 4 expressions with local error:

0.9b
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.6b
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.3b
(* y (log z))
0.1b
(* (- t 1.0) (log a))

rewrite73.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

39.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
22.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
8.0ms
(* (- t 1.0) (log a))

series462.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

226.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
137.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
66.0ms
(* (- t 1.0) (log a))
33.0ms
(* y (log z))

simplify2.9s

Counts
34 → 69
Calls

34 calls. Slowest were:

386.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
296.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
201.0ms
(* (* (* (- t 1.0) (- t 1.0)) (- t 1.0)) (* (* (log a) (log a)) (log a)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
0.5b
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
0.0b
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
0.0b
(* (pow a t) (pow a (- 1.0)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Counts
4 → 118
Calls

4 calls. Slowest were:

32.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
30.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
29.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

513.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
338.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
331.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
143.0ms
(* (pow a t) (pow a (- 1.0)))

simplify9.5s

Counts
103 → 130
Calls

103 calls. Slowest were:

408.0ms
(+ (log (* (pow z y) (exp (- b)))) (+ (log (pow a t)) (* (log a) (- 1.0))))
390.0ms
(+ (log (* (pow z y) (exp (- b)))) (+ (* (log a) t) (* (log a) (- 1.0))))
389.0ms
(+ (log (* (pow z y) (exp (- b)))) (+ (* (log a) t) (log (pow a (- 1.0)))))

prune2.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
0.2b
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
0.2b
(* (pow z y) (pow a t))
0.0b
(* x (* (pow z y) (pow a t)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Counts
4 → 62
Calls

4 calls. Slowest were:

18.0ms
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
18.0ms
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
8.0ms
(* x (* (pow z y) (pow a t)))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

485.0ms
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
417.0ms
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
160.0ms
(* x (* (pow z y) (pow a t)))
101.0ms
(* (pow z y) (pow a t))

simplify4.7s

Counts
36 → 74
Calls

36 calls. Slowest were:

505.0ms
(* (cbrt (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))) (cbrt (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))))
473.0ms
(sqrt (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
397.0ms
(* (exp (* -1 (* (log (/ 1 z)) y))) (* x (exp (* -1 (* t (log (/ 1 a)))))))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (1.9b remaining)

Error of 2.0b against oracle of 0.0b and baseline of 2.0b

bsearch4.0ms

end0.0ms

sample18.2s

Algorithm
intervals