Average Error: 15.2 → 0.8
Time: 12.2s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

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 15.2

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

  3. Applied div-inv15.2

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\]

  4. Applied cbrt-prod0.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]

  5. Final simplification0.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 10.8s)Debug log

sample37.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(cbrt (/ g (* 2 a)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize29.0ms

Local error

Found 1 expressions with local error:

17.1b
(cbrt (/ g (* 2 a)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series100.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

100.0ms
(cbrt (/ g (* 2 a)))

simplify421.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

180.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
177.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
53.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune222.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt (* 2 a))
0.6b
(cbrt g)
0.4b
(/ (cbrt g) (cbrt (* 2 a)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

6.0ms
(/ (cbrt g) (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series766.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

353.0ms
(cbrt (* 2 a))
260.0ms
(cbrt g)
152.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify616.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

209.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
153.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
70.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune628.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* 2 a))
0.6b
(cbrt g)
0.4b
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
0.2b
(/ 1 (cbrt (* 2 a)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))
2.0ms
(/ 1 (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

438.0ms
(/ 1 (cbrt (* 2 a)))
289.0ms
(cbrt (* 2 a))
274.0ms
(cbrt g)
205.0ms
(* (cbrt g) (/ 1 (cbrt (* 2 a))))

simplify739.0ms

Counts
31 → 76
Calls

31 calls. Slowest were:

190.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
153.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
98.0ms
(* g (* (* (/ 1 (cbrt (* 2 a))) (/ 1 (cbrt (* 2 a)))) (/ 1 (cbrt (* 2 a)))))

prune726.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
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))

series897.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

321.0ms
(cbrt (* 2 a))
256.0ms
(cbrt g)
162.0ms
(/ (cbrt (* 2 a)) (cbrt g))
158.0ms
(/ 1 (/ (cbrt (* 2 a)) (cbrt g)))

simplify1.3s

Counts
63 → 99
Calls

63 calls. Slowest were:

254.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
248.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
209.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))

prune842.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes333.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm
intervals