Average Error: 15.4 → 0.9
Time: 11.1s
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 15.4

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

  3. Applied cbrt-div0.9

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

  4. Taylor expanded around 0 34.4

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

  5. Simplified0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019010 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.3s)Debug log

sample81.0ms

Algorithm
intervals

simplify3.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
3.0ms
(cbrt (/ g (* 2 a)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize8.0ms

Local error

Found 1 expressions with local error:

16.1b
(cbrt (/ g (* 2 a)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
4×cbrt-prod
2×add-cube-cbrt
2×*-un-lft-identity
2×add-sqr-sqrt
1×add-log-exp
1×div-inv
1×add-exp-log
1×pow1/3
1×add-cbrt-cube
1×cbrt-div
1×pow1
Counts
1 → 13
Calls
1 calls:
Slowest
1.0ms
(cbrt (/ g (* 2 a)))

series103.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
103.0ms
(cbrt (/ g (* 2 a)))

simplify349.0ms

Counts
8 → 16
Calls
8 calls:
Slowest
161.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
125.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
54.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))
4.0ms
(cbrt (* (cbrt (/ g (* 2 a))) (cbrt (/ g (* 2 a)))))
3.0ms
(cbrt (sqrt (/ g (* 2 a))))

prune156.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b
(cbrt g)
0.6b
(cbrt (* 2 a))
0.3b
(/ (cbrt g) (cbrt (* 2 a)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-cube-cbrt
12×times-frac
12×*-un-lft-identity
12×add-sqr-sqrt
5×add-exp-log
5×cbrt-prod
4×associate-/r*
3×add-log-exp
3×associate-/l*
3×add-cbrt-cube
3×pow1
2×pow1/3
1×div-inv
1×div-exp
1×frac-2neg
1×clear-num
1×cbrt-undiv
Counts
3 → 48
Calls
3 calls:
Slowest
5.0ms
(/ (cbrt g) (cbrt (* 2 a)))
0.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series851.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
380.0ms
(cbrt (* 2 a))
298.0ms
(cbrt g)
173.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify626.0ms

Counts
42 → 57
Calls
42 calls:
Slowest
204.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
183.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
69.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))
17.0ms
(/ (* (cbrt (cbrt g)) (cbrt (cbrt g))) (* (cbrt (cbrt (* 2 a))) (cbrt (cbrt (* 2 a)))))
11.0ms
(/ (* (cbrt (cbrt g)) (cbrt (cbrt g))) 1)

prune605.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

localize1.0ms

Local error

Found 3 expressions with local error:

0.7b
(cbrt g)
0.6b
(cbrt (* 2 a))
0.3b
(/ (cbrt g) (cbrt (* 2 a)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-cube-cbrt
12×times-frac
12×*-un-lft-identity
12×add-sqr-sqrt
5×add-exp-log
5×cbrt-prod
4×associate-/r*
3×add-log-exp
3×associate-/l*
3×add-cbrt-cube
3×pow1
2×pow1/3
1×div-inv
1×div-exp
1×frac-2neg
1×clear-num
1×cbrt-undiv
Counts
3 → 48
Calls
3 calls:
Slowest
6.0ms
(/ (cbrt g) (cbrt (* 2 a)))
1.0ms
(cbrt (* 2 a))
0.0ms
(cbrt g)

series813.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
347.0ms
(cbrt (* 2 a))
283.0ms
(cbrt g)
182.0ms
(/ (cbrt g) (cbrt (* 2 a)))

simplify544.0ms

Counts
42 → 57
Calls
42 calls:
Slowest
163.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
151.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
42.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))
33.0ms
(/ (* (cbrt (cbrt g)) (cbrt (cbrt g))) (* (cbrt (cbrt (* 2 a))) (cbrt (cbrt (* 2 a)))))
16.0ms
(/ (* (cbrt (cbrt g)) (cbrt (cbrt g))) (sqrt (cbrt (* 2 a))))

prune540.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.7b
(cbrt g)
0.6b
(cbrt (/ 1 (* 2 a)))
0.3b
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod
7×add-cube-cbrt
7×associate-*r*
7×*-un-lft-identity
7×add-sqr-sqrt
5×add-exp-log
5×pow1
4×pow1/3
3×add-log-exp
3×associate-*l*
3×add-cbrt-cube
2×div-inv
2×pow-prod-down
2×cbrt-div
1×cbrt-unprod
1×*-commutative
1×associate-*r/
1×prod-exp
Counts
3 → 44
Calls
3 calls:
Slowest
8.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))
1.0ms
(cbrt (/ 1 (* 2 a)))
0.0ms
(cbrt g)

series773.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
320.0ms
(cbrt (/ 1 (* 2 a)))
278.0ms
(cbrt g)
175.0ms
(* (cbrt g) (cbrt (/ 1 (* 2 a))))

simplify555.0ms

Counts
28 → 53
Calls
28 calls:
Slowest
184.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
141.0ms
(* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (* (cbrt -1) (cbrt -1/2)))
72.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))
46.0ms
(* g (/ 1 (* 2 a)))
28.0ms
(* g (/ 1 (* 2 a)))

prune473.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 0.0b

regimes746.0ms

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