Details

sample1.4s

Algorithm

intervals

Results

828.0ms	252×	body	10240	exit
283.0ms	91×	body	2560	valid
118.0ms	85×	body	1280	valid
71.0ms	504×	body	80	nan
33.0ms	37×	body	640	valid
15.0ms	25×	body	320	valid
6.0ms	14×	body	160	valid
1.0ms	4×	body	80	valid
1.0ms	1×	body	320	nan

simplify179.0ms

Calls

1 calls:

Slowest

178.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.4b

localize22.0ms

Local error

Found 2 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
2.3b	(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`

Calls

2 calls:

Slowest

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

series14.0ms

Calls

2 calls:

Slowest

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

simplify183.0ms

Calls

6 calls:

Slowest

76.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
45.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
7.0ms	(fmod (cosh a) (pow a 2))
7.0ms	(fmod (cosh a) (pow a 2))

prune308.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.0b

localize43.0ms

Local error

Found 3 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
13.1b	(log (exp (fmod (cosh a) (* a a))))
2.3b	(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` `add-exp-log` `log-pow`
3×	`expm1-log1p-u` `log-prod` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`
1×	`acos-asin`

Calls

3 calls:

Slowest

6.0ms	(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))

series9.0ms

Calls

3 calls:

Slowest

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

simplify400.0ms

Calls

17 calls:

Slowest

62.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
56.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms	(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))))))
38.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))

prune587.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.0b

localize26.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
11.8b	(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)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

3.0ms	(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

Calls

4 calls:

Slowest

25.0ms	(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)))

simplify607.0ms

Calls

23 calls:

Slowest

66.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms	(exp (sqrt (fmod (cosh a) (* a a))))
47.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
47.0ms	(sqrt (cbrt (fmod (cosh a) (* a a))))
46.0ms	(cbrt (sqrt (fmod (cosh a) (* a a))))

prune785.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 59.0b

localize33.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
11.8b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.3b	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

rewrite23.0ms

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` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`log-prod` `sqrt-prod`
2×	`rem-log-exp` `difference-of-squares`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Calls

4 calls:

Slowest

18.0ms	(- (/ 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))

series46.0ms

Calls

4 calls:

Slowest

30.0ms	(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
12.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify21.5s

Calls

119 calls:

Slowest

685.0ms	(fma (* (cbrt (/ PI 2)) (cbrt (/ PI 2))) (cbrt (/ 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)))))))
443.0ms	(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))))))))
441.0ms	(- (* 1/2 PI) (asin (pow (fmod (cosh a) (pow a 2)) (log1p a))))
386.0ms	(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))))))))
379.0ms	(fma (- (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))))) (* (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)))))))

prune964.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 59.0b

regimes301.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample31.1s

Algorithm

intervals

Results

18.2s	7996×	body	10240	exit
6.2s	3191×	body	2560	valid
2.8s	2531×	body	1280	valid
2.0s	16194×	body	80	nan
1.0s	1217×	body	640	valid
289.0ms	599×	body	320	valid
123.0ms	349×	body	160	valid
17.0ms	113×	body	80	valid
17.0ms	7×	body	5120	nan
9.0ms	7×	body	2560	nan
6.0ms	8×	body	1280	nan
3.0ms	11×	body	160	nan
2.0ms	6×	body	320	nan
2.0ms	4×	body	640	nan