Details

sample2.1s

Algorithm

intervals

Results

1.3s	267×	body	10240	exit
295.0ms	96×	body	2560	valid
144.0ms	70×	body	1280	valid
86.0ms	509×	body	80	nan
52.0ms	55×	body	640	valid
23.0ms	1×	body	320	nan
16.0ms	24×	body	320	valid
5.0ms	9×	body	160	valid
2.0ms	2×	body	1280	nan
0.0ms	2×	body	80	valid

simplify160.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

160.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.9b

localize31.0ms

Local error

Found 2 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
3.5b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

rewrite4.0ms

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

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

8.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify204.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

71.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
50.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
40.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
27.0ms	(fmod (cosh a) (pow a 2))
8.0ms	(fmod (cosh a) (pow a 2))

prune371.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.4b

localize52.0ms

Local error

Found 3 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
12.1b	(log (exp (fmod (cosh a) (* a a))))
3.5b	(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` `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

5.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.0ms	(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	(log (exp (fmod (cosh a) (* a a))))
4.0ms	(fmod (cosh a) (* a a))

simplify464.0ms

Counts

16 → 48

Calls

16 calls:

Slowest

80.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
68.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
51.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
51.0ms	(log (sqrt (exp (fmod (cosh a) (* a a)))))
39.0ms	(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))

prune546.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.4b

localize42.0ms

Local error

Found 4 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
11.5b	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

Slowest

7.0ms	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))
1.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))
1.0ms	(fmod (cosh a) (* a a))

series165.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))
4.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify697.0ms

Counts

18 → 59

Calls

18 calls:

Slowest

129.0ms	(log (sqrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))))))
118.0ms	(log (* (cbrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))))) (cbrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))))
94.0ms	(pow (pow (fmod (cosh a) (pow a 2)) 2) 1/3)
87.0ms	(pow (pow (fmod (cosh a) (pow a 2)) 2) 1/3)
83.0ms	(pow (pow (fmod (cosh a) (pow a 2)) 2) 1/3)

prune756.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.4b

localize72.0ms

Local error

Found 4 expressions with local error:

59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))
59.6b	(fmod (cosh a) (* a a))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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`

Counts

4 → 40

Calls

4 calls:

Slowest

1.0ms	(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))

series15.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

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

simplify136.0ms

Counts

12 → 52

Calls

12 calls:

Slowest

14.0ms	(fmod (cosh a) (pow a 2))
14.0ms	(fmod (cosh a) (pow a 2))
13.0ms	(fmod (cosh a) (pow a 2))
13.0ms	(fmod (cosh a) (pow a 2))
13.0ms	(fmod (cosh a) (pow a 2))

prune884.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 59.4b

regimes392.0ms

Accuracy

0% (0.3b remaining)

Error of 59.4b against oracle of 59.1b and baseline of 59.4b

bsearch2.0ms

end0.0ms

sample33.5s

Algorithm

intervals

Results

19.7s	7896×	body	10240	exit
6.8s	3147×	body	2560	valid
3.0s	2516×	body	1280	valid
2.1s	15855×	body	80	nan
924.0ms	1271×	body	640	valid
321.0ms	635×	body	320	valid
121.0ms	308×	body	160	valid
20.0ms	123×	body	80	valid
12.0ms	5×	body	5120	nan
10.0ms	10×	body	1280	nan
7.0ms	5×	body	2560	nan
3.0ms	6×	body	640	nan
2.0ms	9×	body	160	nan
2.0ms	5×	body	320	nan