Average Error: 0.0 → 0.7
Time: 23.1s
Precision: 64
Internal Precision: 128
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left({c}^{3} \cdot \frac{1}{6} + \left(c + {c}^{5} \cdot \frac{1}{120}\right)\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

  3. Final simplification0.7

    \[\leadsto \left(\left({c}^{3} \cdot \frac{1}{6} + \left(c + {c}^{5} \cdot \frac{1}{120}\right)\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))

Details

Time bar (total: 22.7s)Debug log

sample267.0ms

Algorithm
intervals

simplify32.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

32.0ms
(fmod (sinh c) (- c (pow -2.9807307601812193e+165 2)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

0.0b
(sinh c)

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(sinh c)

series67.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

66.0ms
(sinh c)

simplify124.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

51.0ms
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))
36.0ms
(* 1/2 (- (exp c) (exp (- c))))
35.0ms
(* 1/2 (- (exp c) (exp (* -1 c))))

prune122.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/6 (pow c 3))
0.0b
(* 1/120 (pow c 5))
0.0b
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
3 → 43
Calls

3 calls. Slowest were:

11.0ms
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))
2.0ms
(* 1/6 (pow c 3))
2.0ms
(* 1/120 (pow c 5))

series104.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

40.0ms
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))
36.0ms
(* 1/120 (pow c 5))
29.0ms
(* 1/6 (pow c 3))

simplify382.0ms

Counts
17 → 52
Calls

17 calls. Slowest were:

112.0ms
(* (exp (* 1/6 (pow c 3))) (exp (+ (* 1/120 (pow c 5)) c)))
85.0ms
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))
79.0ms
(+ (* 1/6 (pow c 3)) (+ (* 1/120 (pow c 5)) c))

prune622.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

40.4b
(cbrt (* (* (sinh c) (sinh c)) (sinh c)))
0.1b
(* (* (sinh c) (sinh c)) (sinh c))
0.0b
(* (sinh c) (sinh c))
0.0b
(sinh c)

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 88
Calls

4 calls. Slowest were:

17.0ms
(* (* (sinh c) (sinh c)) (sinh c))
8.0ms
(* (sinh c) (sinh c))
7.0ms
(cbrt (* (* (sinh c) (sinh c)) (sinh c)))

series291.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

77.0ms
(* (sinh c) (sinh c))
77.0ms
(* (* (sinh c) (sinh c)) (sinh c))
74.0ms
(sinh c)
62.0ms
(cbrt (* (* (sinh c) (sinh c)) (sinh c)))

simplify8.5s

Counts
63 → 100
Calls

63 calls. Slowest were:

912.0ms
(* (- (exp c) (exp (- c))) (sinh c))
588.0ms
(* 1/4 (pow (- (exp c) (exp (- c))) 2))
538.0ms
(cbrt (* (* (sinh c) (sinh c)) (- (exp c) (exp (- c)))))

prune955.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch4.0ms

end0.0ms

sample11.1s

Algorithm
intervals