Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	82×	body	1280	valid
6.0ms	139×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
4	34
3	32
2	26
1	19
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize41.0ms

Local error

Found 1 expressions with local error:

1.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`prod-diff`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt`
3×	`fma-neg` `sqrt-prod` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 31

Calls

1 calls:

11.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series859.0ms

Counts

1 → 3

Calls

1 calls:

859.0ms

(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.9s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	3430
2	859
1	301
0	121

prune190.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.8b	(- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
14×	`associate-*r/`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow-prod-down`
6×	`flip3-+` `sqrt-div` `pow-prod-up` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `associate-r` `log1p-expm1-u`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`flip3--` `pow1/2` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `associate-l` `prod-diff` `*-commutative` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

352.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
90.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0ms	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
106.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series12.7s

Counts

4 → 12

Calls

4 calls:

8.5s	(/ (- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.4s	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
773.0ms	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0s	(- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify9.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5003
1	1967
0	564

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.3b

localize101.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))))
0.0b	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.8b	(- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite22.9s

Algorithm

rewrite-expression-head

Rules

132×	`pow1`
68×	`associate-*r/`
60×	`pow-prod-down`
47×	`add-cbrt-cube` `add-exp-log`
31×	`prod-exp` `cbrt-unprod`
30×	`pow-prod-up`
28×	`frac-times`
27×	`flip3-+` `flip-+`
12×	`distribute-rgt-in` `add-sqr-sqrt` `*-un-lft-identity` `distribute-lft-in` `add-cube-cbrt`
9×	`times-frac`
8×	`associate-*l/` `pow-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-plus` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`pow2` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `cube-unmult` `div-exp` `associate-r` `associate-l` `prod-diff` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 157

Calls

4 calls:

0.0ms	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
17.0s	(/ (- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))))
327.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.6s	(- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series1.8m

Counts

4 → 12

Calls

4 calls:

582.0ms	(fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.6m	(/ (- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))))
422.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.8s	(- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify2.1m

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
1	4763
0	1336

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.3b

localize118.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(* (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))) (+ (* (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0))))) (+ (* (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (* (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
0.5b	(pow (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
0.8b	(- (pow (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) 3) (pow (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

rewrite5.2m

Algorithm

rewrite-expression-head

Calls

2 calls:

3.5s

(pow (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)

67.0ms

(- (pow (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) 3) (pow (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))