Average Error: 1.9 → 1.9
Time: 1.0m
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 2018362 
(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: 33.5s)Debug log

start851.0ms

Algorithm
intervals

setup798.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.8b
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.7b
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.3b
(* y (log z))
0.1b
(* (- t 1.0) (log a))

rewrite46.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

20.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
14.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
8.0ms
(* (- t 1.0) (log a))

series457.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

205.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
121.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
76.0ms
(* (- t 1.0) (log a))
55.0ms
(* y (log z))

simplify3.1s

Counts
34 → 69
Calls

34 calls. Slowest were:

354.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
345.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
206.0ms
(* (* (* (- t 1.0) (- t 1.0)) (- t 1.0)) (* (* (log a) (log a)) (log a)))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))
0.7b
(/ (* x (exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))) y)
0.3b
(* (log z) y)
0.1b
(* (- t 1.0) (log a))

rewrite57.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

34.0ms
(exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))
17.0ms
(/ (* x (exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))) y)
4.0ms
(* (- t 1.0) (log a))

series527.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

234.0ms
(/ (* x (exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))) y)
159.0ms
(exp (- (+ (* (log z) y) (* (- t 1.0) (log a))) b))
72.0ms
(* (log z) y)
62.0ms
(* (- t 1.0) (log a))

simplify3.0s

Counts
33 → 69
Calls

33 calls. Slowest were:

339.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
299.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
200.0ms
(* (- (* t t) (* 1.0 1.0)) (log a))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
0.7b
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
0.2b
(* (pow z y) (exp (- b)))
0.1b
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Counts
4 → 115
Calls

4 calls. Slowest were:

45.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
40.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
36.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

553.0ms
(/ (* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))) y)
328.0ms
(* x (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
304.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
77.0ms
(* (pow z y) (exp (- b)))

simplify9.9s

Counts
100 → 127
Calls

100 calls. Slowest were:

423.0ms
(+ (log (* (pow z y) (exp (- b)))) (+ (log (pow a t)) (* (log a) (- 1.0))))
413.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
394.0ms
(+ (+ (* (log z) y) (- b)) (+ (* (log a) t) (* (log a) (- 1.0))))

prune2.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
0.5b
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
0.2b
(* (pow z y) (pow a t))
0.0b
(* (exp b) (pow a 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

17.0ms
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
16.0ms
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
7.0ms
(* (exp b) (pow a 1.0))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

410.0ms
(/ (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))) y)
390.0ms
(/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
152.0ms
(* (exp b) (pow a 1.0))
126.0ms
(* (pow z y) (pow a t))

simplify4.7s

Counts
43 → 82
Calls

43 calls. Slowest were:

548.0ms
(sqrt (/ (* x (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
462.0ms
(* (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)))))
452.0ms
(/ (* (* (* x (* (pow z y) (pow a t))) (* x (* (pow z y) (pow a t)))) (* x (* (pow z y) (pow a t)))) (* (* (* (exp b) (exp b)) (exp b)) (* (* (pow a 1.0) (pow a 1.0)) (pow a 1.0))))

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes951.0ms

Accuracy

0% (1.9b remaining)

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

bsearch3.0ms