Details

sample1.4s

Algorithm

intervals

Results

831.0ms	266×	body	10240	exit
228.0ms	97×	body	2560	valid
120.0ms	79×	body	1280	valid
93.0ms	512×	body	80	nan
38.0ms	48×	body	640	valid
9.0ms	13×	body	320	valid
4.0ms	11×	body	160	valid
2.0ms	8×	body	80	valid
1.0ms	2×	body	640	nan
0.0ms	1×	body	160	nan

simplify89.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

89.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize20.0ms

Local error

Found 2 expressions with local error:

58.2b	(fmod (cosh a) (* a a))
1.8b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

rewrite13.0ms

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`

Counts

2 → 21

Calls

2 calls:

Slowest

10.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series13.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

10.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify184.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

81.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
38.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
8.0ms	(fmod (cosh a) (pow a 2))
7.0ms	(fmod (cosh a) (pow a 2))

prune353.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.0b

localize46.0ms

Local error

Found 3 expressions with local error:

58.2b	(fmod (cosh a) (* a a))
12.5b	(log (exp (fmod (cosh a) (* a a))))
1.8b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

rewrite9.0ms

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`

Counts

3 → 39

Calls

3 calls:

Slowest

5.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series12.0ms

Counts

3 → 9

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))))

simplify370.0ms

Counts

16 → 48

Calls

16 calls:

Slowest

61.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
59.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
52.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
37.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune664.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 58.0b

localize31.0ms

Local error

Found 4 expressions with local error:

58.2b	(fmod (cosh a) (* a a))
58.2b	(fmod (cosh a) (* a a))
11.5b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.8b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite11.0ms

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`

Counts

4 → 52

Calls

4 calls:

Slowest

6.0ms	(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)))
1.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series27.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

16.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
4.0ms	(fmod (cosh a) (* a a))
3.0ms	(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)))

simplify627.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

75.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
75.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
60.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
53.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
45.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))

prune789.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 58.0b

localize50.0ms

Local error

Found 4 expressions with local error:

58.2b	(fmod (cosh a) (* a a))
58.2b	(fmod (cosh a) (* a a))
58.2b	(fmod (cosh a) (* a a))
11.6b	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-pow`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-pow1`
6×	`pow1` `log-prod` `exp-prod` `sqrt-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `rem-log-exp`

Counts

4 → 56

Calls

4 calls:

Slowest

4.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series155.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify813.0ms

Counts

26 → 68

Calls

26 calls:

Slowest

66.0ms	(log (sqrt (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a))))))))
64.0ms	(log (sqrt (sqrt (exp (sqrt (fmod (cosh a) (* a a)))))))
58.0ms	(log (* (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a)))))) (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))))
54.0ms	(/ (cbrt (sqrt (fmod (cosh a) (* a a)))) 2)
54.0ms	(/ (sqrt (sqrt (fmod (cosh a) (* a a)))) 2)

prune863.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 57.9b

regimes672.0ms

Accuracy

0% (0.2b remaining)

Error of 59.4b against oracle of 59.2b and baseline of 59.4b

bsearch6.0ms

end0.0ms

sample35.9s

Algorithm

intervals

Results

20.8s	7942×	body	10240	exit
7.7s	3262×	body	2560	valid
3.0s	2513×	body	1280	valid
2.1s	15986×	body	80	nan
946.0ms	1182×	body	640	valid
514.0ms	317×	body	160	valid
366.0ms	620×	body	320	valid
19.0ms	106×	body	80	valid
14.0ms	5×	body	5120	nan
10.0ms	11×	body	1280	nan
8.0ms	6×	body	2560	nan
5.0ms	7×	body	640	nan
3.0ms	10×	body	160	nan
2.0ms	6×	body	320	nan