Details

sample104.0ms

Algorithm

intervals

Results

26.0ms	570×	body	80	nan
25.0ms	244×	body	160	nan
15.0ms	256×	body	80	valid

simplify25.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize40.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.3b	(sqrt (- (* x x) 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

21.0ms	(+ x (sqrt (- (* x x) 1.0)))
21.0ms	(sqrt (- (* x x) 1.0))

series163.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(+ x (sqrt (- (* x x) 1.0)))
84.0ms	(sqrt (- (* x x) 1.0))

simplify861.0ms

Counts: 34 → 34

prune145.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`sqrt-prod`
14×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
5×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`associate-r/` `associate-l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 69

Calls

3 calls:

21.0ms	(sqrt (+ x (sqrt 1.0)))
11.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
86.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series617.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(sqrt (+ x (sqrt 1.0)))
215.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
331.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify735.0ms

Counts: 78 → 78

prune406.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0)))))
0.5b	(* (* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0))))) (sqrt (- x (sqrt 1.0))))
0.5b	(cbrt (+ x (sqrt 1.0)))
0.5b	(cbrt (+ x (sqrt 1.0)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`associate-r`
16×	`sqrt-prod`
14×	`sqrt-div`
13×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
6×	`flip3-+` `flip-+`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `flip--` `distribute-lft-out` `unswap-sqr`
2×	`pow1/3` `associate-l/` `-commutative` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

43.0ms	(* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0)))))
85.0ms	(* (* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0))))) (sqrt (- x (sqrt 1.0))))
11.0ms	(cbrt (+ x (sqrt 1.0)))
11.0ms	(cbrt (+ x (sqrt 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0)))))
546.0ms	(* (* (fabs (cbrt (+ x (sqrt 1.0)))) (sqrt (cbrt (+ x (sqrt 1.0))))) (sqrt (- x (sqrt 1.0))))
166.0ms	(cbrt (+ x (sqrt 1.0)))
210.0ms	(cbrt (+ x (sqrt 1.0)))

simplify1.3s

Counts: 101 → 101

prune732.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify41.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	7506×	body	160	nan
950.0ms	16177×	body	80	nan
531.0ms	8000×	body	80	valid