Details

sample1.5s

Algorithm

intervals

Results

828.0ms	248×	body	10240	exit
303.0ms	102×	body	2560	valid
122.0ms	509×	body	80	nan
109.0ms	71×	body	1280	valid
43.0ms	44×	body	640	valid
14.0ms	20×	body	320	valid
4.0ms	10×	body	160	valid
2.0ms	9×	body	80	valid
1.0ms	1×	body	320	nan
1.0ms	1×	body	640	nan
0.0ms	1×	body	160	nan

simplify115.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

115.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize36.0ms

Local error

Found 3 expressions with local error:

58.6b	(fmod (cosh a) (* a a))
2.3b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0b	(cosh a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`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` `cosh-def`

Counts

3 → 32

Calls

3 calls:

Slowest

2.0ms	(cosh a)
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series100.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

87.0ms	(cosh a)
10.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify484.0ms

Counts

9 → 41

Calls

9 calls:

Slowest

172.0ms	(* 1/2 (+ (exp (* -1 a)) (exp a)))
68.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
58.0ms	(+ (* 1/2 (pow a 2)) (+ (* 1/24 (pow a 4)) 1))
56.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
45.0ms	(* 1/2 (+ (exp a) (exp (- a))))

prune465.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.1b

localize23.0ms

Local error

Found 4 expressions with local error:

58.6b	(fmod (cosh a) (* a a))
11.5b	(log (exp (fmod (cosh a) (* a a))))
2.3b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0b	(cosh a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

Slowest

5.0ms	(cosh a)
2.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series52.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

45.0ms	(cosh a)
3.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(fmod (cosh a) (* a a))

simplify576.0ms

Counts

19 → 62

Calls

19 calls:

Slowest

185.0ms	(* 1/2 (+ (exp (* -1 a)) (exp a)))
55.0ms	(+ (* 1/2 (pow a 2)) (+ (* 1/24 (pow a 4)) 1))
54.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune892.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 58.0b

localize40.0ms

Local error

Found 4 expressions with local error:

58.6b	(fmod (cosh a) (* a a))
58.6b	(fmod (cosh a) (* a a))
10.6b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.3b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite12.0ms

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

7.0ms	(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))

series36.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

23.0ms	(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)))
4.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify608.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

68.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
54.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
49.0ms	(sqrt (cbrt (fmod (cosh a) (* a a))))
47.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
45.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune988.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 58.0b

localize48.0ms

Local error

Found 4 expressions with local error:

58.6b	(fmod (cosh a) (* a a))
58.6b	(fmod (cosh a) (* a a))
58.6b	(fmod (cosh a) (* a a))
10.7b	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))

rewrite10.0ms

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

8.0ms	(log (sqrt (exp (sqrt (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))

series192.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify730.0ms

Counts

26 → 68

Calls

26 calls:

Slowest

72.0ms	(log (* (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a)))))) (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))))
59.0ms	(/ (sqrt (cbrt (fmod (cosh a) (* a a)))) 2)
57.0ms	(/ (sqrt (sqrt (fmod (cosh a) (* a a)))) 2)
53.0ms	(sqrt (exp (sqrt (fmod (cosh a) (* a a)))))
50.0ms	(log (sqrt (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a))))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 58.0b

regimes466.0ms

Accuracy

0% (0.2b remaining)

Error of 59.1b against oracle of 59.0b and baseline of 59.1b

bsearch7.0ms

end0.0ms

sample34.1s

Algorithm

intervals

Results

19.2s	7881×	body	10240	exit
6.6s	3183×	body	2560	valid
3.3s	2550×	body	1280	valid
3.1s	16084×	body	80	nan
828.0ms	1217×	body	640	valid
335.0ms	593×	body	320	valid
128.0ms	323×	body	160	valid
24.0ms	134×	body	80	valid
11.0ms	9×	body	2560	nan
10.0ms	4×	body	5120	nan
8.0ms	10×	body	1280	nan
5.0ms	9×	body	640	nan
4.0ms	9×	body	320	nan
2.0ms	8×	body	160	nan