Details

sample1.3s

Algorithm

intervals

Results

645.0ms	240×	body	10240	exit
316.0ms	107×	body	2560	valid
110.0ms	91×	body	1280	valid
43.0ms	494×	body	80	nan
22.0ms	29×	body	640	valid
9.0ms	18×	body	320	valid
4.0ms	1×	body	5120	nan
2.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	44	10
4	89	10
5	195	10
6	633	10
7	2582	10
done	5000	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh a)
0.0b	(log1p a)
1.5b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
58.8b	(fmod (cosh a) (* a a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `log1p-udef` `cosh-def` `log1p-expm1`

Counts

4 → 40

Calls

4 calls:

3.0ms	(cosh a)
3.0ms	(log1p a)
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series157.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cosh a)
48.0ms	(log1p a)
14.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
9.0ms	(fmod (cosh a) (* a a))

simplify4.8s

Counts

52 → 52

Iterations

Useful iterations: 4 (788.0ms)

Iter	Nodes	Cost
0	90	436
1	161	425
2	310	384
3	657	383
4	1514	376
5	3936	376
done	5000	376

prune309.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 58.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p a)
1.5b	(acos (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
3.7b	(log (exp (log1p a)))
58.8b	(fmod (cosh a) (* a a))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

1.0ms	(log1p a)
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
7.0ms	(log (exp (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series102.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(log1p a)
7.0ms	(acos (pow (fmod (cosh a) (* a a)) (log (exp (log1p a)))))
40.0ms	(log (exp (log1p a)))
5.0ms	(fmod (cosh a) (* a a))

simplify4.4s

Counts

59 → 59

Iterations

Useful iterations: 4 (458.0ms)

Iter	Nodes	Cost
0	88	550
1	144	473
2	259	428
3	504	426
4	1093	412
5	2718	412
done	5000	412

prune291.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 58.9b

localize42.0ms

Local error

Found 4 expressions with local error:

1.5b	(acos (pow (fmod (cosh a) (* a a)) (+ (* 2 (log (cbrt (exp (log1p a))))) (log (cbrt (exp (log1p a)))))))
3.8b	(log (cbrt (exp (log1p a))))
3.8b	(log (cbrt (exp (log1p a))))
58.8b	(fmod (cosh a) (* a a))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

2.0ms	(acos (pow (fmod (cosh a) (* a a)) (+ (* 2 (log (cbrt (exp (log1p a))))) (log (cbrt (exp (log1p a)))))))
6.0ms	(log (cbrt (exp (log1p a))))
6.0ms	(log (cbrt (exp (log1p a))))
1.0ms	(fmod (cosh a) (* a a))

series221.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(acos (pow (fmod (cosh a) (* a a)) (+ (* 2 (log (cbrt (exp (log1p a))))) (log (cbrt (exp (log1p a)))))))
97.0ms	(log (cbrt (exp (log1p a))))
113.0ms	(log (cbrt (exp (log1p a))))
5.0ms	(fmod (cosh a) (* a a))

simplify2.9s

Counts

67 → 67

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	95	868
1	174	709
2	356	601
3	778	571
4	2441	565
done	5000	557

prune530.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 58.9b

localize46.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (cbrt (exp (log1p a)))))
3.6b	(log (sqrt (cbrt (exp (log1p a)))))
3.8b	(log (cbrt (exp (log1p a))))
58.8b	(fmod (cosh a) (* a a))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
10×	`log-pow`
9×	`pow1` `cbrt-prod`
7×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `rem-log-exp`
2×	`pow1/2`

Counts

4 → 73

Calls

4 calls:

8.0ms	(log (sqrt (cbrt (exp (log1p a)))))
9.0ms	(log (sqrt (cbrt (exp (log1p a)))))
7.0ms	(log (cbrt (exp (log1p a))))
1.0ms	(fmod (cosh a) (* a a))

series334.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(log (sqrt (cbrt (exp (log1p a)))))
87.0ms	(log (sqrt (cbrt (exp (log1p a)))))
125.0ms	(log (cbrt (exp (log1p a))))
5.0ms	(fmod (cosh a) (* a a))

simplify3.1s

Counts

85 → 85

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	120	903
1	222	834
2	455	762
3	935	756
4	2015	747
done	5000	720

prune605.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 58.9b

regimes194.0ms

Accuracy

75% (0.4b remaining)

Error of 59.0b against oracle of 58.6b and baseline of 60.1b

bsearch243.0ms

Steps

Iters	Range		Point
8	4.907784520098122e-166	1.096458200021764e-161	1.542338768776222e-162

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	35
1	22	35
done	22	35

end0.0ms

sample36.1s

Algorithm

intervals

Results

21.2s	7715×	body	10240	exit
7.9s	3175×	body	2560	valid
2.8s	2518×	body	1280	valid
2.0s	16132×	body	80	nan
823.0ms	1260×	body	640	valid
310.0ms	634×	body	320	valid
135.0ms	299×	body	160	valid
21.0ms	8×	body	5120	nan
17.0ms	114×	body	80	valid
17.0ms	13×	body	2560	nan
9.0ms	12×	body	1280	nan
4.0ms	8×	body	640	nan
3.0ms	9×	body	320	nan
0.0ms	2×	body	160	nan