Details

sample1.8s

Algorithm

intervals

Results

938.0ms	251×	body	10240	exit
340.0ms	104×	body	2560	valid
147.0ms	73×	body	1280	valid
87.0ms	48×	body	640	valid
86.0ms	485×	body	80	nan
16.0ms	20×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	3×	body	80	valid

simplify74.0ms

Calls

1 calls:

Slowest

73.0ms

(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.8b

localize24.0ms

Local error

Found 2 expressions with local error:

60.1b	(fmod (cosh a) (* a a))
1.9b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin`

Calls

2 calls:

Slowest

1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series12.0ms

Calls

2 calls:

Slowest

9.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify156.0ms

Calls

6 calls:

Slowest

56.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
41.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
23.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
12.0ms	(fmod (cosh a) (pow a 2))
12.0ms	(fmod (cosh a) (pow a 2))

prune349.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.4b

localize22.0ms

Local error

Found 3 expressions with local error:

60.1b	(fmod (cosh a) (* a a))
9.7b	(log (exp (fmod (cosh a) (* a a))))
1.9b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `log-pow`
3×	`expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `rem-log-exp`

Calls

3 calls:

Slowest

9.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series12.0ms

Calls

3 calls:

Slowest

5.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(log (exp (fmod (cosh a) (* a a))))

simplify329.0ms

Calls

16 calls:

Slowest

65.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
54.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
44.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
37.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
25.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune602.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.4b

localize30.0ms

Local error

Found 4 expressions with local error:

60.1b	(fmod (cosh a) (* a a))
60.1b	(fmod (cosh a) (* a a))
9.0b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.9b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
6×	`exp-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `sqrt-prod`
1×	`acos-asin` `rem-log-exp`

Calls

4 calls:

Slowest

3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series20.0ms

Calls

4 calls:

Slowest

13.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify573.0ms

Calls

22 calls:

Slowest

69.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
49.0ms	(sqrt (cbrt (fmod (cosh a) (* a a))))
47.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))
43.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune540.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.4b

localize41.0ms

Local error

Found 4 expressions with local error:

60.1b	(fmod (cosh a) (* a a))
60.1b	(fmod (cosh a) (* a a))
60.1b	(fmod (cosh a) (* a a))
60.1b	(fmod (cosh a) (* a a))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

1.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series18.0ms

Calls

4 calls:

Slowest

4.0ms	(fmod (cosh a) (* a a))
4.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify149.0ms

Calls

12 calls:

Slowest

12.0ms	(fmod (cosh a) (pow a 2))
12.0ms	(fmod (cosh a) (pow a 2))
12.0ms	(fmod (cosh a) (pow a 2))
12.0ms	(fmod (cosh a) (pow a 2))
12.0ms	(fmod (cosh a) (pow a 2))

prune886.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 59.4b

regimes328.0ms

Accuracy

0% (0.2b remaining)

Error of 59.2b against oracle of 59.1b and baseline of 59.2b

bsearch6.0ms

end0.0ms

sample35.4s

Algorithm

intervals

Results

20.9s	8071×	body	10240	exit
7.7s	3263×	body	2560	valid
2.9s	2449×	body	1280	valid
2.0s	16127×	body	80	nan
932.0ms	1215×	body	640	valid
326.0ms	630×	body	320	valid
109.0ms	313×	body	160	valid
22.0ms	130×	body	80	valid
19.0ms	6×	body	5120	nan
13.0ms	9×	body	2560	nan
8.0ms	10×	body	1280	nan
5.0ms	11×	body	320	nan
4.0ms	7×	body	640	nan
2.0ms	8×	body	160	nan