Details

sample597.0ms

Algorithm

intervals

Results

457.0ms	241×	body	10240	exit
50.0ms	71×	body	1280	valid
17.0ms	43×	body	640	valid
9.0ms	169×	body	80	nan
8.0ms	3×	body	2560	valid
7.0ms	98×	body	80	valid
7.0ms	28×	body	320	valid
2.0ms	13×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	5	5
1	11	5
2	14	5
3	16	5
done	16	5

prune55.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(cosh c)
36.3b	(fmod (cosh c) (log1p a))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cosh-def`

Counts

2 → 19

Calls

2 calls:

4.0ms	(cosh c)
2.0ms	(fmod (cosh c) (log1p a))

series94.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(cosh c)
17.0ms	(fmod (cosh c) (log1p a))

simplify2.8s

Counts

25 → 25

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	44	159
1	79	156
2	200	142
3	662	142
4	3333	142
done	5001	142

prune128.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh c)
0.0b	(cosh c)
0.0b	(* (sqrt (cosh c)) (sqrt (cosh c)))
36.3b	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `cosh-def` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(cosh c)
1.0ms	(cosh c)
16.0ms	(* (sqrt (cosh c)) (sqrt (cosh c)))
0.0ms	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

series224.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cosh c)
61.0ms	(cosh c)
90.0ms	(* (sqrt (cosh c)) (sqrt (cosh c)))
5.0ms	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

simplify1.3s

Counts

95 → 95

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	94	868
1	191	530
2	852	483
done	5000	480

prune264.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c)))
0.0b	(log1p (cosh c))
0.0b	(expm1 (log1p (cosh c)))
36.4b	(fmod (* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c))) (log1p a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`sqrt-pow1` `pow1/2`
1×	`log1p-udef` `expm1-log1p` `cosh-def` `sqrt-unprod` `sqrt-div` `log1p-expm1` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `expm1-udef`

Counts

4 → 64

Calls

4 calls:

27.0ms	(* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c)))
1.0ms	(log1p (cosh c))
1.0ms	(expm1 (log1p (cosh c)))
1.0ms	(fmod (* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c))) (log1p a))

series744.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c)))
184.0ms	(log1p (cosh c))
204.0ms	(expm1 (log1p (cosh c)))
10.0ms	(fmod (* (sqrt (expm1 (log1p (cosh c)))) (sqrt (cosh c))) (log1p a))

simplify3.4s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	123	850
1	244	532
2	829	439
3	3770	428
done	5001	428

prune389.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 30.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (log1p (cosh c))))
0.0b	(log (log1p (cosh c)))
0.0b	(expm1 (exp (log (log1p (cosh c)))))
36.4b	(fmod (* (sqrt (expm1 (exp (log (log1p (cosh c)))))) (sqrt (cosh c))) (log1p a))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

7.0ms	(exp (log (log1p (cosh c))))
13.0ms	(log (log1p (cosh c)))
1.0ms	(expm1 (exp (log (log1p (cosh c)))))
1.0ms	(fmod (* (sqrt (expm1 (exp (log (log1p (cosh c)))))) (sqrt (cosh c))) (log1p a))

series782.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(exp (log (log1p (cosh c))))
369.0ms	(log (log1p (cosh c)))
221.0ms	(expm1 (exp (log (log1p (cosh c)))))
9.0ms	(fmod (* (sqrt (expm1 (exp (log (log1p (cosh c)))))) (sqrt (cosh c))) (log1p a))

simplify1.7s

Counts

63 → 63

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	114	665
1	208	498
2	552	392
3	2531	387
done	5000	382

prune375.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 30.5b

regimes322.0ms

Accuracy

0% (1.7b remaining)

Error of 33.8b against oracle of 32.1b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
done	7	7

end0.0ms

sample18.9s

Algorithm

intervals

Results

13.2s	7746×	body	10240	exit
2.0s	2250×	body	1280	valid
1.1s	1606×	body	640	valid
762.0ms	5172×	body	80	nan
317.0ms	2830×	body	80	valid
202.0ms	131×	body	2560	valid
170.0ms	785×	body	320	valid
63.0ms	388×	body	160	valid
24.0ms	10×	body	5120	valid