Average Error: 34.2 → 33.8
Time: 41.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\frac{\left(\sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}} \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}\right) \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.2

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
  2. Using strategy rm

  3. Applied cosh-def34.2

    \[\leadsto \left(\color{blue}{\left(\frac{e^{c} + e^{-c}}{2}\right)} \bmod \left(\log_* (1 + a)\right)\right)\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt34.1

    \[\leadsto \left(\left(\frac{\color{blue}{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)\]
  6. Using strategy rm

  7. Applied add-cube-cbrt33.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt33.8

    \[\leadsto \left(\sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\frac{\color{blue}{\left(\sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}} \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}\right) \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

  10. Final simplification33.8

    \[\leadsto \left(\sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\frac{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\frac{\left(\sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}} \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}\right) \cdot \sqrt[3]{\sqrt{e^{c} + e^{-c}} \cdot \sqrt{e^{c} + e^{-c}}}}{2}\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 38.2s)Debug log

sample782.0ms

Algorithm
intervals

simplify15.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

14.0ms
(fmod (cosh c) (log1p a))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize25.0ms

Local error

Found 2 expressions with local error:

40.7b
(fmod (cosh c) (log1p a))
0.0b
(cosh c)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 15
Calls

2 calls. Slowest were:

1.0ms
(fmod (cosh c) (log1p a))
1.0ms
(cosh c)

series96.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

59.0ms
(cosh c)
37.0ms
(fmod (cosh c) (log1p a))

simplify444.0ms

Counts
6 → 21
Calls

6 calls. Slowest were:

389.0ms
(* 1/2 (+ (exp (* -1 c)) (exp c)))
34.0ms
(* 1/2 (+ (exp c) (exp (- c))))
14.0ms
(+ (* 1/2 (pow c 2)) (+ (* 1/24 (pow c 4)) 1))

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.9b

localize32.0ms

Local error

Found 2 expressions with local error:

40.7b
(fmod (/ (+ (exp c) (exp (- c))) 2) (log1p a))
0.0b
(+ (exp c) (exp (- c)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 19
Calls

2 calls. Slowest were:

5.0ms
(+ (exp c) (exp (- c)))
0.0ms
(fmod (/ (+ (exp c) (exp (- c))) 2) (log1p a))

series29.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

25.0ms
(+ (exp c) (exp (- c)))
4.0ms
(fmod (/ (+ (exp c) (exp (- c))) 2) (log1p a))

simplify112.0ms

Counts
8 → 25
Calls

8 calls. Slowest were:

28.0ms
(fmod (* 1/2 (+ (exp c) (exp (- c)))) (log1p a))
26.0ms
(fmod (* 1/2 (+ (exp (* -1 c)) (exp c))) (log1p a))
23.0ms
(fmod (* 1/2 (+ (exp c) (exp (- c)))) (log1p a))

prune430.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 34.8b

localize26.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
1.0b
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))
0.2b
(sqrt (+ (exp c) (exp (- c))))
0.2b
(sqrt (+ (exp c) (exp (- c))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Counts
4 → 77
Calls

4 calls. Slowest were:

29.0ms
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))
10.0ms
(sqrt (+ (exp c) (exp (- c))))
10.0ms
(sqrt (+ (exp c) (exp (- c))))

series144.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

50.0ms
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))
47.0ms
(sqrt (+ (exp c) (exp (- c))))
39.0ms
(sqrt (+ (exp c) (exp (- c))))
8.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))

simplify4.9s

Counts
63 → 89
Calls

63 calls. Slowest were:

400.0ms
(* (sqrt (+ (pow (exp c) 3) (pow (exp (- c)) 3))) (sqrt (- (* (exp c) (exp c)) (* (exp (- c)) (exp (- c))))))
399.0ms
(* (* (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) (sqrt (+ (exp c) (exp (- c))))) (* (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) (sqrt (+ (exp c) (exp (- c))))))
371.0ms
(* (sqrt (- (* (exp c) (exp c)) (* (exp (- c)) (exp (- c))))) (sqrt (+ (pow (exp c) 3) (pow (exp (- c)) 3))))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 34.7b

localize25.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
40.7b
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
40.7b
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
1.0b
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 61
Calls

4 calls. Slowest were:

29.0ms
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))
0.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
0.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))

series66.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

45.0ms
(* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c)))))
7.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
7.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))
7.0ms
(fmod (/ (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) 2) (log1p a))

simplify3.7s

Counts
49 → 73
Calls

49 calls. Slowest were:

417.0ms
(* (* (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) (sqrt (+ (exp c) (exp (- c))))) (* (* (sqrt (+ (exp c) (exp (- c)))) (sqrt (+ (exp c) (exp (- c))))) (sqrt (+ (exp c) (exp (- c))))))
407.0ms
(* (sqrt (- (* (exp c) (exp c)) (* (exp (- c)) (exp (- c))))) (sqrt (+ (pow (exp c) 3) (pow (exp (- c)) 3))))
311.0ms
(* (sqrt (+ (pow (exp c) 3) (pow (exp (- c)) 3))) (sqrt (- (* (exp c) (exp c)) (* (exp (- c)) (exp (- c))))))

prune1.3s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 34.5b

regimes952.0ms

Accuracy

0% (1.1b remaining)

Error of 33.8b against oracle of 32.7b and baseline of 33.8b

bsearch3.0ms

end0.0ms

sample23.6s

Algorithm
intervals