Average Error: 0.1 → 0.1
Time: 48.7s
Precision: 64
Internal Precision: 128
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\frac{rand}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}} \cdot \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right)\]

Error

Bits error versus a

Bits error versus rand

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
  2. Using strategy rm

  3. Applied associate-*l/0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \color{blue}{\frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\right)\]

  4. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{\color{blue}{rand}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}\right)\]
  5. Using strategy rm

  6. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) \cdot 1 + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\]

  7. Final simplification0.1

    \[\leadsto \frac{rand}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}} \cdot \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019005 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))

Details

Time bar (total: 47.9s)Debug log

sample419.0ms

Algorithm
intervals

simplify404.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

404.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

4.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
3.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
2.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series177.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

77.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
47.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
30.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
23.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify6.3s

Counts
50 → 85
Calls

50 calls. Slowest were:

472.0ms
(* (+ a (/ 1.0 3.0)) (+ (* 1 1) (- (* (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)) (* 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))))
429.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
401.0ms
(- (* 1/3 (* (sqrt -3.0) rand)) (+ (* 4.5 (/ (* (pow a 2) rand) (sqrt -3.0))) (+ (* 1.5 (/ (* a rand) (sqrt -3.0))) (* 3.375 (/ (* (pow a 2) rand) (pow (sqrt -3.0) 3))))))

prune758.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

5.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
2.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series170.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

63.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
46.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
32.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
29.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify5.0s

Counts
52 → 83
Calls

52 calls. Slowest were:

504.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (+ (pow 1 3) (pow (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) 3)))
379.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
359.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))

prune807.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.2b
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

8.0ms
(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
2.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series192.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

75.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
66.0ms
(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))
34.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
17.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify3.6s

Counts
48 → 81
Calls

48 calls. Slowest were:

481.0ms
(* (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))) (* (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
381.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) rand)
338.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))

prune838.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.2b
(* (/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) rand)
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 165
Calls

4 calls. Slowest were:

14.0ms
(* (/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) rand)
10.0ms
(/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
3.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))

series717.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

432.0ms
(/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
146.0ms
(* (/ (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) rand)
102.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
37.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify18.8s

Counts
180 → 177
Calls

180 calls. Slowest were:

520.0ms
(/ (/ 1 (sqrt (sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3)))))) (* (cbrt (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (cbrt (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))))
495.0ms
(/ (/ 1 (sqrt (sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3)))))) (sqrt (sqrt 9)))
493.0ms
(+ (* 0.017361111111111112 (* (pow (/ 1 (pow a 9)) 1/4) (/ 1 (sqrt 3)))) (+ (* 0.08333333333333333 (* (pow (/ 1 (pow a 5)) 1/4) (/ 1 (sqrt 3)))) (* (pow (/ 1 a) 1/4) (/ 1 (sqrt 3)))))

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch5.0ms

end0.0ms

sample6.9s

Algorithm
intervals