Details

sample1.4s

Algorithm

intervals

Results

837.0ms	248×	body	10240	exit
308.0ms	115×	body	2560	valid
97.0ms	68×	body	1280	valid
64.0ms	468×	body	80	nan
60.0ms	43×	body	640	valid
9.0ms	15×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	8×	body	80	valid
1.0ms	1×	body	640	nan

simplify143.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

143.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize20.0ms

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)))

rewrite7.0ms

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

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

12.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify187.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

52.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
48.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
22.0ms	(fmod (cosh a) (pow a 2))
7.0ms	(fmod (cosh a) (pow a 2))

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 58.7b

localize26.0ms

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)))

rewrite4.0ms

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

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))

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))))

simplify365.0ms

Counts

16 → 48

Calls

16 calls:

Slowest

48.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
39.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
38.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
37.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
36.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune591.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.7b

localize56.0ms

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)))

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

23.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
6.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify631.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

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)))))))
58.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
52.0ms	(cbrt (sqrt (fmod (cosh a) (* a a))))
43.0ms	(sqrt (sqrt (fmod (cosh a) (* a a))))

prune770.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 58.7b

localize48.0ms

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))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`log-prod` `sqrt-prod`
2×	`difference-of-squares`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 112

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))))
3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series81.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

54.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
20.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
4.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify21.9s

Counts

118 → 124

Calls

118 calls:

Slowest

663.0ms	(fma (sqrt (/ PI 2)) (sqrt (/ PI 2)) (- (* (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))))
455.0ms	(fma (* (cbrt (/ PI 2)) (cbrt (/ PI 2))) (cbrt (/ PI 2)) (- (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))))
448.0ms	(fma (sqrt (/ PI 2)) (sqrt (/ PI 2)) (- (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))))
436.0ms	(fma (/ (sqrt PI) (sqrt 2)) (/ (sqrt PI) (sqrt 2)) (- (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))))
409.0ms	(fma (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (/ (cbrt PI) (cbrt 2)) (- (* (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))) 1)))

prune927.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 58.7b

regimes545.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample31.3s

Algorithm

intervals

Results

18.0s	7839×	body	10240	exit
6.2s	3207×	body	2560	valid
2.8s	2508×	body	1280	valid
2.0s	15960×	body	80	nan
1.1s	1227×	body	640	valid
546.0ms	607×	body	320	valid
103.0ms	334×	body	160	valid
30.0ms	12×	body	5120	nan
18.0ms	117×	body	80	valid
9.0ms	7×	body	2560	nan
8.0ms	10×	body	1280	nan
4.0ms	7×	body	640	nan
2.0ms	5×	body	320	nan
1.0ms	5×	body	160	nan