Details

sample1.4s

Algorithm

intervals

Results

778.0ms	248×	body	10240	exit
311.0ms	115×	body	2560	valid
102.0ms	68×	body	1280	valid
85.0ms	468×	body	80	nan
36.0ms	43×	body	640	valid
8.0ms	15×	body	320	valid
3.0ms	7×	body	160	valid
2.0ms	8×	body	80	valid
1.0ms	1×	body	640	nan

simplify122.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

122.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize24.0ms

Local error

Found 2 expressions with local error:

58.9b	(fmod (cosh a) (* a a))
1.7b	(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))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify215.0ms

Counts

6 → 23

Calls

6 calls:

Slowest

72.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
58.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
56.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
12.0ms	(fmod (cosh a) (pow a 2))
7.0ms	(fmod (cosh a) (pow a 2))

prune291.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 58.7b

localize32.0ms

Local error

Found 3 expressions with local error:

58.9b	(fmod (cosh a) (* a a))
9.6b	(log (exp (fmod (cosh a) (* a a))))
1.7b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

rewrite8.0ms

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))

series12.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

5.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
4.0ms	(fmod (cosh a) (* a a))
3.0ms	(log (exp (fmod (cosh a) (* a a))))

simplify351.0ms

Counts

16 → 42

Calls

16 calls:

Slowest

72.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
66.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
44.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
42.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
26.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.7b

localize37.0ms

Local error

Found 4 expressions with local error:

58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))
8.9b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.7b	(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

6.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series27.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

18.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
5.0ms	(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))

simplify586.0ms

Counts

22 → 56

Calls

22 calls:

Slowest

73.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
54.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))

prune719.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 58.7b

localize37.0ms

Local error

Found 4 expressions with local error:

58.9b	(fmod (cosh a) (* a a))
58.9b	(fmod (cosh a) (* a a))
8.9b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.2b	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

rewrite33.0ms

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

22.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
10.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series64.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

35.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
22.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
4.0ms	(fmod (cosh a) (* a a))
4.0ms	(fmod (cosh a) (* a a))

simplify3.2s

Counts

29 → 64

Calls

29 calls:

Slowest

361.0ms	(- (sqrt (/ PI 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
355.0ms	(/ (exp (/ PI 2)) (exp (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
326.0ms	(- (/ (sqrt PI) (sqrt 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))
324.0ms	(- (* 1/2 PI) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
267.0ms	(+ (sqrt (/ PI 2)) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))

prune736.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 58.7b

regimes384.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample36.9s

Algorithm

intervals

Results

20.4s	7839×	body	10240	exit
7.6s	3207×	body	2560	valid
3.9s	2508×	body	1280	valid
2.6s	15960×	body	80	nan
1.2s	1227×	body	640	valid
325.0ms	607×	body	320	valid
148.0ms	334×	body	160	valid
35.0ms	12×	body	5120	nan
22.0ms	117×	body	80	valid
10.0ms	7×	body	2560	nan
10.0ms	10×	body	1280	nan
4.0ms	7×	body	640	nan
2.0ms	5×	body	320	nan
2.0ms	5×	body	160	nan