Average Error: 1.9 → 1.9
Time: 45.3s
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 1.9

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

  2. Taylor expanded around 0 1.9

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

  3. Simplified1.9

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

  4. Final simplification1.9

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

Reproduce

herbie shell --seed 2019004 
(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: 43.9s)Debug log

sample641.0ms

Algorithm
intervals

simplify419.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

419.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

34.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
23.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
8.0ms
(* (- t 1.0) (log a))

series424.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

195.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
152.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
45.0ms
(* (- t 1.0) (log a))
32.0ms
(* y (log z))

simplify3.2s

Counts
34 → 69
Calls

34 calls. Slowest were:

474.0ms
(* (- (log -1) (log (/ -1 z))) y)
378.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
281.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

24.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
18.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
8.0ms
(* (- t 1.0) (log a))

series458.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

205.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
166.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
54.0ms
(* (- t 1.0) (log a))
32.0ms
(* y (log z))

simplify2.7s

Counts
34 → 69
Calls

34 calls. Slowest were:

361.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
222.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
188.0ms
(* (* (* (- 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

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) y)
0.5b
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))
0.1b
(pow a (- t 1.0))
0.0b
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 72
Calls

4 calls. Slowest were:

23.0ms
(/ (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) y)
16.0ms
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))
15.0ms
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))

series811.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

310.0ms
(/ (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) y)
246.0ms
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))
199.0ms
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))
55.0ms
(pow a (- t 1.0))

simplify5.1s

Counts
51 → 84
Calls

51 calls. Slowest were:

426.0ms
(* (* (* (* (pow a (- t 1.0)) (pow a (- t 1.0))) (pow a (- t 1.0))) (* (* (pow z y) (pow z y)) (pow z y))) (* (* (exp (- b)) (exp (- b))) (exp (- b))))
424.0ms
(* x (* (* (pow a t) (pow z y)) (exp (- b))))
334.0ms
(* (exp (* -1 b)) (* (exp (* (- (log -1) (log (/ -1 z))) y)) (exp (* -1 (* (- (log -1) (log (/ -1 a))) (- 1.0 t))))))

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) (/ 1 y))
0.5b
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))
0.1b
(pow a (- t 1.0))
0.0b
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Counts
4 → 85
Calls

4 calls. Slowest were:

54.0ms
(* (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) (/ 1 y))
14.0ms
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))
12.0ms
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))

series864.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

306.0ms
(* (* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))) (/ 1 y))
234.0ms
(* (* (pow a (- t 1.0)) (pow z y)) (exp (- b)))
223.0ms
(* x (* (* (pow a (- t 1.0)) (pow z y)) (exp (- b))))
101.0ms
(pow a (- t 1.0))

simplify6.7s

Counts
70 → 97
Calls

70 calls. Slowest were:

386.0ms
(* (* x (* (pow a (- t 1.0)) (pow z y))) (/ 1 y))
385.0ms
(* x (* (exp (* -1 b)) (* (exp (* (- (log -1) (log (/ -1 z))) y)) (exp (* -1 (* (- (log -1) (log (/ -1 a))) (- 1.0 t)))))))
384.0ms
(* (* x (* (* (pow a t) (pow z y)) (exp (- b)))) 1)

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes1.0s

Accuracy

0% (1.9b remaining)

Error of 1.9b against oracle of 0.0b and baseline of 1.9b

bsearch4.0ms

end0.0ms

sample15.7s

Algorithm
intervals