Average Error: 1.9 → 1.9
Time: 46.7s
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

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

  3. 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 2019008 
(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: 45.6s)Debug log

sample718.0ms

Algorithm
intervals

simplify393.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

393.0ms
(/ (* 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: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

38.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
4.0ms
(* (- t 1.0) (log a))

series485.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

230.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
124.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
78.0ms
(* (- t 1.0) (log a))
53.0ms
(* y (log z))

simplify2.8s

Counts
34 → 69
Calls

34 calls. Slowest were:

320.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
284.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
226.0ms
(* (* (* (- t 1.0) (- t 1.0)) (- t 1.0)) (* (* (log a) (log a)) (log a)))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

59.0ms
(exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))
31.0ms
(/ (* x (exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))) y)
8.0ms
(* (- t 1.0) (log a))

series549.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

210.0ms
(/ (* x (exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))) y)
188.0ms
(exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))
85.0ms
(* (log z) y)
66.0ms
(* (- t 1.0) (log a))

simplify2.7s

Counts
33 → 69
Calls

33 calls. Slowest were:

277.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
270.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
224.0ms
(/ (* x (exp (- (* 1.0 (log (/ 1 a))) (+ (* (log (/ 1 z)) y) (+ b (* t (log (/ 1 a)))))))) y)

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
0.8b
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
0.0b
(* (pow a t) (pow a (- 1.0)))
0.0b
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Counts
4 → 118
Calls

4 calls. Slowest were:

50.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
39.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
34.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

494.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
345.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
314.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
148.0ms
(* (pow a t) (pow a (- 1.0)))

simplify8.3s

Counts
103 → 130
Calls

103 calls. Slowest were:

363.0ms
(+ (+ (* (log z) y) (- b)) (+ (* (log a) t) (* (log a) (- 1.0))))
361.0ms
(+ (log (* (pow z y) (exp (- b)))) (+ (* (log a) t) (* (log a) (- 1.0))))
358.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))

prune2.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* x (* (pow z y) (pow a t))) (* y (* (exp b) (pow a 1.0))))
0.2b
(* (pow z y) (pow a t))
0.0b
(* (exp b) (pow a 1.0))
0.0b
(* x (* (pow z y) (pow a t)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Counts
4 → 60
Calls

4 calls. Slowest were:

18.0ms
(/ (* x (* (pow z y) (pow a t))) (* y (* (exp b) (pow a 1.0))))
9.0ms
(* x (* (pow z y) (pow a t)))
7.0ms
(* (exp b) (pow a 1.0))

series903.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

413.0ms
(/ (* x (* (pow z y) (pow a t))) (* y (* (exp b) (pow a 1.0))))
198.0ms
(* (exp b) (pow a 1.0))
147.0ms
(* x (* (pow z y) (pow a t)))
145.0ms
(* (pow z y) (pow a t))

simplify2.9s

Counts
36 → 72
Calls

36 calls. Slowest were:

561.0ms
(/ (* (* (* x (* (pow z y) (pow a t))) (* x (* (pow z y) (pow a t)))) (* x (* (pow z y) (pow a t)))) (* (* (* y (* (exp b) (pow a 1.0))) (* y (* (exp b) (pow a 1.0)))) (* y (* (exp b) (pow a 1.0)))))
388.0ms
(* (exp (* -1 (* (log (/ 1 z)) y))) (* x (exp (* -1 (* t (log (/ 1 a)))))))
349.0ms
(- (log (* x (* (pow z y) (pow a t)))) (log (* y (* (exp b) (pow a 1.0)))))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes749.0ms

Accuracy

0% (1.8b remaining)

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

bsearch2.0ms

end0.0ms

sample17.3s

Algorithm
intervals