Average Error: 15.0 → 0.9
Time: 11.0s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied cbrt-div0.9

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]

  4. Final simplification0.9

    \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

Reproduce

herbie shell --seed 2019004 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.6s)Debug log

sample77.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

4.0ms
(cbrt (/ g (* 2 a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 1 expressions with local error:

18.1b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

1.0ms
(cbrt (/ g (* 2 a)))

series133.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

133.0ms
(cbrt (/ g (* 2 a)))

simplify413.0ms

Counts
8 → 16
Calls

8 calls. Slowest were:

218.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
130.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
50.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune151.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt (* 2 a))
0.5b
(cbrt g)
0.3b
(/ (cbrt g) (cbrt (* 2 a)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

3.0ms
(/ (cbrt g) (cbrt (* 2 a)))
0.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series770.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

313.0ms
(cbrt (* 2 a))
293.0ms
(cbrt g)
164.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify583.0ms

Counts
42 → 57
Calls

42 calls. Slowest were:

183.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
152.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
55.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune552.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt (/ 1 (* 2 a)))
0.5b
(cbrt g)
0.3b
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

7.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))
1.0ms
(cbrt (/ 1 (* 2 a)))
0.0ms
(cbrt g)

series706.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

298.0ms
(cbrt (/ 1 (* 2 a)))
275.0ms
(cbrt g)
134.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

simplify498.0ms

Counts
28 → 53
Calls

28 calls. Slowest were:

186.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
134.0ms
(* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (* (cbrt -1) (cbrt -1/2)))
45.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune482.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* 2 a))
0.5b
(cbrt g)
0.3b
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
0.3b
(/ (cbrt (* 2 a)) (cbrt g))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

6.0ms
(/ (cbrt (* 2 a)) (cbrt g))
3.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
1.0ms
(cbrt (* 2 a))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

340.0ms
(cbrt (* 2 a))
306.0ms
(cbrt g)
207.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))
156.0ms
(/ (cbrt (* 2 a)) (cbrt g))

simplify950.0ms

Counts
63 → 91
Calls

63 calls. Slowest were:

163.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
162.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
158.0ms
(/ (* (cbrt -2) (exp (* 1/3 (- (log (/ -1 g)) (log (/ -1 a)))))) (cbrt -1))

prune762.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 0.0b

regimes435.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
intervals