Details

sample129.0ms

Algorithm

intervals

Results

48.0ms	281×	body	160	nan
28.0ms	569×	body	80	nan
16.0ms	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

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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:

16.0ms	(+ x (sqrt (- (* x x) 1.0)))
14.0ms	(sqrt (- (* x x) 1.0))

series178.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(+ x (sqrt (- (* x x) 1.0)))
93.0ms	(sqrt (- (* x x) 1.0))

simplify793.0ms

Counts

41 → 41

Iterations

Iter	Nodes
done	5001
2	970
1	240
0	94

prune202.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

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))))

rewrite72.0ms

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:

8.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
62.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

series469.0ms

Counts

2 → 6

Calls

2 calls:

190.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
279.0ms	(* (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

prune768.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.1b	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.1b	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.5b	(* (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
12.0ms	(* (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

series1.6s

Counts

4 → 12

Calls

4 calls:

608.0ms	(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
309.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
300.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
349.0ms	(* (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) (sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1747
1	458
0	180

prune673.0ms

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

sample3.8s

Algorithm

intervals

Results

1.1s	16122×	body	80	nan
1.0s	8000×	body	80	valid
924.0ms	7472×	body	160	nan