Details

sample121.0ms

Algorithm

intervals

Results

73.0ms	287×	body	80	valid
19.0ms	85×	body	80	nan

simplify179.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	160
7	160
6	159
5	152
4	140
3	108
2	63
1	36
0	20

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize168.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* c a) (* b b))
1.0b	(fma -4 (* c a) (* b b))
24.5b	(sqrt (fma -4 (* c a) (* b b)))
24.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma -4 (* c a) (* b b))
0.0ms	(fma -4 (* c a) (* b b))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma -4 (* c a) (* b b))
75.0ms	(fma -4 (* c a) (* b b))
100.0ms	(sqrt (fma -4 (* c a) (* b b)))
106.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	2002
4	2002
3	454
2	127
1	61
0	41

prune499.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.2b

localize145.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
0.5b	(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0b	(fma -4 (* c a) (* b b))
24.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

33.0ms	(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
0.0ms	(fma -4 (* c a) (* b b))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
94.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
68.0ms	(fma -4 (* c a) (* b b))
137.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts

191 → 191

Iterations

Iter	Nodes
done	2003
3	2003
2	1578
1	619
0	278

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize161.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a)
1.0b	(fma -4 (* c a) (* b b))
8.4b	(- (/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a) (/ (/ b 2) a))
24.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5326×	`add-sqr-sqrt`
5300×	`*-un-lft-identity`
5274×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div` `associate-/l/`

Counts

4 → 3262

Calls

4 calls:

8.0ms	(/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a)
0.0ms	(fma -4 (* c a) (* b b))
45.0ms	(- (/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a) (/ (/ b 2) a))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series958.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a)
69.0ms	(fma -4 (* c a) (* b b))
146.0ms	(- (/ (/ (sqrt (fma -4 (* c a) (* b b))) 2) a) (/ (/ b 2) a))
582.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify4.9s

Counts

3274 → 3274

Iterations

Iter	Nodes
done	3161
0	3161

prune36.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.2b

localize128.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* c a) (* b b))
14.2b	(- (/ (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 1) (/ a (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 2))) (/ (/ b 2) a))
24.5b	(sqrt (fma -4 (* c a) (* b b)))
24.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite25.2s

Algorithm

rewrite-expression-head

Rules

688726×	`times-frac`
310502×	`add-sqr-sqrt`
309936×	`*-un-lft-identity`
309879×	`add-cube-cbrt`
227067×	`sqrt-prod`
130849×	`prod-diff`
21984×	`div-inv`
3043×	`fma-neg`
1408×	`associate-/r/`
108×	`difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `fma-udef` `flip--`

Counts

4 → 134062

Calls

4 calls:

0.0ms	(fma -4 (* c a) (* b b))
1.2s	(- (/ (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 1) (/ a (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 2))) (/ (/ b 2) a))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma -4 (* c a) (* b b))
105.0ms	(- (/ (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 1) (/ a (/ (sqrt (sqrt (fma -4 (* c a) (* b b)))) 2))) (/ (/ b 2) a))
83.0ms	(sqrt (fma -4 (* c a) (* b b)))
102.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify4.1m

Counts

134074 → 134074

Iterations

Iter	Nodes
done	89865
0	89865

Details

sample121.0ms

simplify179.0ms

prune11.0ms

localize168.0ms

rewrite5.0ms

series348.0ms

simplify1.1s

prune499.0ms

localize145.0ms

rewrite58.0ms

series385.0ms

simplify1.2s

prune1.2s

localize161.0ms

rewrite341.0ms

series958.0ms

simplify4.9s

prune36.1s

localize128.0ms

rewrite25.2s

series345.0ms

simplify4.1m

prune4.7m