Details

sample72.0ms

Algorithm

intervals

Results

20.0ms	569×	body	80	nan
18.0ms	281×	body	160	nan
10.0ms	256×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.3b	(sqrt (- (* x x) 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

27.0ms	(+ x (sqrt (- (* x x) 1.0)))
11.0ms	(sqrt (- (* x x) 1.0))

series141.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(+ x (sqrt (- (* x x) 1.0)))
56.0ms	(sqrt (- (* x x) 1.0))

simplify616.0ms

Counts

41 → 41

Iterations

Iter	Nodes
done	5001
2	970
1	240
0	94

prune233.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l` `add-cube-cbrt`
6×	`pow1`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`fma-def` `flip3--` `pow-prod-down` `flip--`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 60

Calls

2 calls:

9.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
59.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

series546.0ms

Counts

2 → 6

Calls

2 calls:

230.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
316.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

simplify1.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1604
1	402
0	163

prune301.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
5.8b	(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

0.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
3.0ms	(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

series712.0ms

Counts

2 → 6

Calls

2 calls:

372.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
339.0ms	(exp (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

simplify1.6s

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
3	3325
2	666
1	206
0	90

prune232.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	16122×	body	80	nan
805.0ms	7472×	body	160	nan
609.0ms	8000×	body	80	valid