Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	231×	body	160	nan
12.0ms	565×	body	80	nan
8.0ms	256×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.8b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

9.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
9.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(sqrt (- (* x x) 1.0))

series322.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
69.0ms	(+ x (sqrt (- (* x x) 1.0)))
55.0ms	(sqrt (- (* x x) 1.0))

simplify1.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (671.0ms)

Iter	Nodes	Cost
0	146	832
1	337	748
2	948	682
3	3628	614
done	5000	614

prune158.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (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))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 76

Calls

3 calls:

2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
29.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series642.0ms

Counts

3 → 9

Calls

3 calls:

292.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
151.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
198.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.1s

Counts

85 → 85

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	197	1683
1	467	1428
2	1370	1310
done	5000	1286

prune251.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

484×	`sqrt-div`
144×	`frac-times`
107×	`sqrt-prod`
89×	`pow1`
84×	`sqrt-pow1`
68×	`add-sqr-sqrt`
63×	`pow-prod-down`
61×	`flip3--` `flip--`
60×	`flip3-+` `flip-+`
48×	`associate-r/` `associate-l/`
42×	`pow1/2`
28×	`*-un-lft-identity`
25×	`associate-r`
21×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `unswap-sqr`
12×	`pow-prod-up`
10×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr`
7×	`sqrt-unprod`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `distribute-lft-out--`
2×	`rem-sqrt-square` `pow-plus` `distribute-lft-out`
1×	`pow2` `swap-sqr` `rem-square-sqrt`

Counts

4 → 274

Calls

4 calls:

7.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
99.0ms	(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))
38.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
36.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

184.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
195.0ms	(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))
352.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
351.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))

simplify1.2s

Counts

286 → 286

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	464	9955
1	1240	7390
2	3528	6641
done	5000	6632

prune877.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	16	30
done	16	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

373.0ms	7787×	body	160	nan
350.0ms	16432×	body	80	nan
234.0ms	8000×	body	80	valid