Average Error: 15.6 → 0.8
Time: 14.1s
Precision: 64
Internal Precision: 128
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}\]

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 15.6

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

  2. Initial simplification15.6

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

  4. Applied cbrt-div0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 9.3s)Debug log

start95.0ms

Algorithm
intervals

setup36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize19.0ms

Local error

Found 1 expressions with local error:

16.0b
(cbrt (/ g (* a 2)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

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

series151.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

150.0ms
(cbrt (/ g (* a 2)))

simplify610.0ms

Counts
8 → 18
Calls

8 calls. Slowest were:

332.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))))
194.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
68.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune159.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* a 2))
0.4b
(/ (cbrt g) (cbrt (* a 2)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

5.0ms
(/ (cbrt g) (cbrt (* a 2)))
0.0ms
(cbrt (* a 2))
0.0ms
(cbrt g)

series777.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

328.0ms
(cbrt (* a 2))
308.0ms
(cbrt g)
140.0ms
(/ (cbrt g) (cbrt (* a 2)))

simplify852.0ms

Counts
42 → 63
Calls

42 calls. Slowest were:

414.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
207.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))
70.0ms
(/ (exp (* 1/3 (- (log g) (log a)))) (cbrt 2))

prune718.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt g)
0.5b
(cbrt (* a 2))
0.3b
(/ (cbrt (* a 2)) (cbrt g))
0.2b
(/ 1 (/ (cbrt (* a 2)) (cbrt g)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

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

series927.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

310.0ms
(cbrt (* a 2))
302.0ms
(cbrt g)
169.0ms
(/ 1 (/ (cbrt (* a 2)) (cbrt g)))
146.0ms
(/ (cbrt (* a 2)) (cbrt g))

simplify1.3s

Counts
63 → 99
Calls

63 calls. Slowest were:

423.0ms
(/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (cbrt -1)) (cbrt -2))
196.0ms
(* (exp (* 1/3 (- (log (/ 1 g)) (log (/ 1 a))))) (cbrt 2))
163.0ms
(/ (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))) (cbrt 2))

prune1.1s

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 50
Calls

3 calls. Slowest were:

8.0ms
(* (cbrt g) (cbrt (/ 1 (* a 2))))
1.0ms
(cbrt (/ 1 (* a 2)))
0.0ms
(cbrt g)

series759.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

323.0ms
(cbrt (/ 1 (* a 2)))
296.0ms
(cbrt g)
139.0ms
(* (cbrt g) (cbrt (/ 1 (* a 2))))

simplify890.0ms

Counts
28 → 59
Calls

28 calls. Slowest were:

396.0ms
(* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 g))))) (* (cbrt -1) (cbrt -1/2)))
190.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 a)) (log (/ 1 g))))))
76.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log g) (log a)))))

prune648.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.0b

regimes211.0ms

Accuracy

0% (0.8b remaining)

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

bsearch1.0ms