Details

sample44.0ms

Algorithm

intervals

Results

11.0ms	565×	body	80	nan
10.0ms	231×	body	160	nan
7.0ms	256×	body	80	valid

simplify4.0ms

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))

rewrite27.0ms

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:

12.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
9.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(sqrt (- (* x x) 1.0))

series314.0ms

Counts

3 → 9

Calls

3 calls:

198.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
66.0ms	(+ x (sqrt (- (* x x) 1.0)))
49.0ms	(sqrt (- (* x x) 1.0))

simplify1.9s

Counts

61 → 61

Iterations

Useful iterations: 3 (453.0ms)

Iter	Nodes	Cost
0	146	832
1	340	752
2	1056	682
3	4857	614
done	5000	614

prune164.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

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))))

rewrite42.0ms

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))))))
3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
33.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series796.0ms

Counts

3 → 9

Calls

3 calls:

391.0ms	(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)))))
253.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify617.0ms

Counts

85 → 85

Iterations

Useful iterations: done (613.0ms)

Iter	Nodes	Cost
0	197	1683
1	477	1435
2	1591	1310
done	5000	1308

prune297.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

116×	`sqrt-div`
62×	`sqrt-prod`
36×	`add-sqr-sqrt`
32×	`frac-times`
26×	`*-un-lft-identity`
23×	`flip3-+` `flip-+`
20×	`pow1` `associate-l`
16×	`add-cube-cbrt` `associate-*r/`
13×	`sqrt-pow1`
12×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r` `pow-prod-down` `associate-*l/`
9×	`pow1/2`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 153

Calls

4 calls:

8.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
8.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
68.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
41.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series983.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
158.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
300.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
384.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify1.4s

Counts

165 → 165

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	311	3869
1	820	3132
2	3114	2900
done	5000	2894

prune655.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	16	22
done	16	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

388.0ms	7787×	body	160	nan
380.0ms	16432×	body	80	nan
251.0ms	8000×	body	80	valid