Details

sample1.4s

Algorithm

intervals

Results

711.0ms	235×	body	10240	exit
280.0ms	106×	body	2560	valid
113.0ms	71×	body	1280	valid
64.0ms	492×	body	80	nan
25.0ms	30×	body	640	valid
19.0ms	32×	body	320	valid
5.0ms	11×	body	160	valid
1.0ms	6×	body	80	valid
1.0ms	1×	body	2560	nan
1.0ms	1×	body	640	nan

simplify133.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

132.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize19.0ms

Local error

Found 2 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
2.9b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 17

Calls

2 calls:

Slowest

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

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

simplify223.0ms

Counts

6 → 23

Calls

6 calls:

Slowest

73.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
61.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
24.0ms	(fmod (cosh a) (pow a 2))
14.0ms	(fmod (cosh a) (pow a 2))

prune308.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 58.6b

localize42.0ms

Local error

Found 3 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
11.6b	(log (exp (fmod (cosh a) (* a a))))
2.9b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 33

Calls

3 calls:

Slowest

4.0ms	(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))

series7.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

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

simplify387.0ms

Counts

16 → 42

Calls

16 calls:

Slowest

75.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
53.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
50.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
46.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
39.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune529.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 58.6b

localize34.0ms

Local error

Found 4 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
10.5b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.9b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

Slowest

5.0ms	(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))

series29.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

20.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms	(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)))

simplify577.0ms

Counts

22 → 56

Calls

22 calls:

Slowest

64.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
54.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
52.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
48.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))
43.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))

prune894.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 58.6b

localize42.0ms

Local error

Found 4 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
10.5b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.6b	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`log-pow` `add-cube-cbrt`
6×	`exp-prod` `add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`log-prod` `sqrt-prod`
2×	`difference-of-squares`
1×	`asin-acos` `sub-neg` `times-frac` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 52

Calls

4 calls:

Slowest

20.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
16.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series58.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

40.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
13.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify3.5s

Counts

29 → 64

Calls

29 calls:

Slowest

621.0ms	(- (* 1/2 PI) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
328.0ms	(- (sqrt (/ PI 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
297.0ms	(+ (/ (sqrt PI) (sqrt 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
291.0ms	(- (/ (sqrt PI) (sqrt 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
288.0ms	(- (* 1/2 PI) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))

prune845.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 58.6b

regimes457.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample33.4s

Algorithm

intervals

Results

19.3s	7905×	body	10240	exit
7.4s	3171×	body	2560	valid
3.1s	2464×	body	1280	valid
1.8s	15757×	body	80	nan
936.0ms	1296×	body	640	valid
300.0ms	637×	body	320	valid
102.0ms	310×	body	160	valid
41.0ms	122×	body	80	valid
20.0ms	8×	body	5120	nan
7.0ms	5×	body	2560	nan
6.0ms	7×	body	1280	nan
4.0ms	7×	body	640	nan
2.0ms	7×	body	160	nan
1.0ms	3×	body	320	nan