Average Error: 0.1 → 0.1
Time: 49.2s
Precision: 64
Internal Precision: 128
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}{rand}}\right)\]

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 clear-num0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2018362 
(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: 32.5s)Debug log

start546.0ms

Algorithm
intervals

setup438.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

7.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
7.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
3.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series595.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

442.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
87.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
36.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
30.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify7.2s

Counts
50 → 85
Calls

50 calls. Slowest were:

596.0ms
(* (+ 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)))))
539.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
496.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b
(/ rand (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)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

14.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
3.0ms
(* 9 (- a (/ 1.0 3.0)))
2.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series157.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

60.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
44.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
35.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
18.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify5.6s

Counts
52 → 83
Calls

52 calls. Slowest were:

442.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
422.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (+ (pow 1 3) (pow (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) 3)))
405.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
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 → 72
Calls

4 calls. Slowest were:

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

series251.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

87.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
85.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
41.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))))
36.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify6.8s

Counts
47 → 84
Calls

47 calls. Slowest were:

485.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))))
453.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
449.0ms
(* (+ 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))))))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3 (sqrt (- a (/ 1.0 3.0))))
0.2b
(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

10.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
2.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))
1.0ms
(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))

series150.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

51.0ms
(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
43.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
29.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))
27.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify5.0s

Counts
51 → 82
Calls

51 calls. Slowest were:

539.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ 1 (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
380.0ms
(* (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
328.0ms
(- (* 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))))))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes160.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms