Average Error: 1.9 → 1.9
Time: 45.6s
Precision: 64
Internal Precision: 128
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x}{\frac{y}{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}\]

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. Using strategy rm

  3. Applied associate-/l*1.9

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

  4. Final simplification1.9

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(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: 44.4s)Debug log

sample567.0ms

Algorithm
intervals

simplify329.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

328.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize49.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.0b
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.3b
(* y (log z))
0.1b
(* (- t 1.0) (log a))

rewrite44.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

26.0ms
(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))

series427.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

213.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
118.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
50.0ms
(* (- t 1.0) (log a))
45.0ms
(* y (log z))

simplify3.1s

Counts
34 → 77
Calls

34 calls. Slowest were:

324.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
303.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
217.0ms
(* (* (* (- t 1.0) (- t 1.0)) (- t 1.0)) (* (* (log a) (log a)) (log a)))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Counts
4 → 67
Calls

4 calls. Slowest were:

33.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
15.0ms
(/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
5.0ms
(/ x (/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))

series576.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

213.0ms
(/ x (/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))
193.0ms
(/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
115.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
55.0ms
(* y (log z))

simplify4.5s

Counts
36 → 79
Calls

36 calls. Slowest were:

354.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
325.0ms
(cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
317.0ms
(sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))) y)
0.2b
(* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))
0.2b
(fma t (log a) (- b))
0.1b
(* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
4 → 63
Calls

4 calls. Slowest were:

16.0ms
(* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))
14.0ms
(* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b)))))
14.0ms
(/ (* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))) y)

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

420.0ms
(/ (* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))) y)
346.0ms
(* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b))))
331.0ms
(* x (* (* (pow a (- 1.0)) (pow z y)) (exp (fma t (log a) (- b)))))
51.0ms
(fma t (log a) (- b))

simplify5.6s

Counts
32 → 75
Calls

32 calls. Slowest were:

538.0ms
(* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b)))))
438.0ms
(+ (+ (* (log a) (- 1.0)) (* (log z) y)) (fma t (log a) (- b)))
409.0ms
(+ (+ (* (log a) (- 1.0)) (log (pow z y))) (fma t (log a) (- b)))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0)) y)
0.2b
(fma t (log a) (- b))
0.0b
(/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0))
0.0b
(* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
4 → 63
Calls

4 calls. Slowest were:

10.0ms
(/ (/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0)) y)
9.0ms
(/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0))
7.0ms
(* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b)))))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

526.0ms
(/ (/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0)) y)
356.0ms
(/ (* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b))))) (pow a 1.0))
194.0ms
(* x (* (* 1 (pow z y)) (exp (fma t (log a) (- b)))))
85.0ms
(fma t (log a) (- b))

simplify4.0s

Counts
32 → 75
Calls

32 calls. Slowest were:

370.0ms
(/ (* (exp (* -1 (* (log (/ 1 z)) y))) (* x (exp (- (+ b (* t (log (/ 1 a)))))))) (* a y))
344.0ms
(* (exp (* -1 (* (log (/ 1 z)) y))) (* x (exp (- (+ b (* t (log (/ 1 a))))))))
306.0ms
(/ (* (* 1 (pow z y)) (exp (fma t (log a) (- b)))) (pow a 1.0))

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes1000.0ms

Accuracy

0% (1.9b remaining)

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

bsearch3.0ms

end0.0ms

sample16.5s

Algorithm
intervals