Average Error: 2.0 → 1.9
Time: 52.1s
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 2.0

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  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 2018365 
(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: 24.0s)Debug log

start969.0ms

Algorithm
intervals

setup408.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

1.1b
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
0.8b
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.2b
(* y (log z))
0.2b
(* (- t 1.0) (log a))

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 57
Calls

4 calls. Slowest were:

19.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
10.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
4.0ms
(* (- t 1.0) (log a))

series395.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

168.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
132.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
64.0ms
(* (- t 1.0) (log a))
31.0ms
(* y (log z))

simplify2.9s

Counts
34 → 69
Calls

34 calls. Slowest were:

342.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
315.0ms
(- (+ (* 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)))

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 61
Calls

4 calls. Slowest were:

41.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
7.0ms
(* (- t 1.0) (log a))
4.0ms
(/ x (/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))

series422.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

161.0ms
(/ x (/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))
155.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
68.0ms
(* (- t 1.0) (log a))
37.0ms
(* y (log z))

simplify4.2s

Counts
39 → 73
Calls

39 calls. Slowest were:

705.0ms
(+ (* t (* (log a) (exp (- (* 1.0 (log a)))))) (+ (exp (- (* 1.0 (log a)))) (* (log z) (* (exp (- (* 1.0 (log a)))) y))))
350.0ms
(- (+ (* t (log -1)) (* 1.0 (log (/ -1 a)))) (+ (* t (log (/ -1 a))) (* 1.0 (log -1))))
287.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
4 → 99
Calls

4 calls. Slowest were:

13.0ms
(/ y (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
13.0ms
(/ x (/ y (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))))
10.0ms
(* (pow z y) (exp (- b)))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

527.0ms
(/ x (/ y (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))))
419.0ms
(/ y (* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0)))))
157.0ms
(* (pow a t) (pow a (- 1.0)))
76.0ms
(* (pow z y) (exp (- b)))

simplify3.9s

Counts
73 → 111
Calls

73 calls. Slowest were:

389.0ms
(- (* a y) (+ (* a (* (log z) (pow y 2))) (* a (* t (* y (log a))))))
342.0ms
(* (* (pow z y) (exp (- b))) (* (pow a t) (pow a (- 1.0))))
329.0ms
(+ (* 1/2 (* (pow (/ 1 (pow a 1.0)) 1.0) (* (pow t 2) (pow (log a) 2)))) (+ (* (pow (/ 1 (pow a 1.0)) 1.0) (* t (log a))) (pow (/ 1 (pow a 1.0)) 1.0)))

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

3.0ms
(* (exp b) (pow a 1.0))
3.0ms
(/ x (* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
3.0ms
(* (pow z y) (pow a t))

series915.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

420.0ms
(/ x (* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
232.0ms
(* (exp b) (pow a 1.0))
177.0ms
(/ y (* (pow z y) (pow a t)))
86.0ms
(* (pow z y) (pow a t))

simplify2.1s

Counts
33 → 71
Calls

33 calls. Slowest were:

347.0ms
(+ (* (pow (/ 1 (pow a 1.0)) 1.0) (/ (* x (* t (log a))) y)) (+ (* (pow (/ 1 (pow a 1.0)) 1.0) (* x (log z))) (* (pow (/ 1 (pow a 1.0)) 1.0) (/ x y))))
260.0ms
(/ y (* (exp (* -1 (* (log (/ 1 z)) y))) (exp (* -1 (* t (log (/ 1 a)))))))
248.0ms
(* (exp (* -1 (* (log (/ 1 z)) y))) (exp (* -1 (* t (log (/ 1 a))))))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes859.0ms

Accuracy

0% (1.8b remaining)

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

bsearch2.0ms