Details

sample45.0ms

Algorithm

intervals

Results

26.0ms

275×

body

valid

simplify78.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	80
5	80
4	76
3	56
2	40
1	21
0	11

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.5b	(- (* b c) (* a d))
24.7b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma d d (* c c))
8.0ms	(- (* b c) (* a d))
15.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(fma d d (* c c))
60.0ms	(- (* b c) (* a d))
113.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify981.0ms

Counts

67 → 67

Iterations

Iter	Nodes
3	3064
2	803
1	229
0	95

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
27.8b	(sqrt (fma d d (* c c)))
27.8b	(sqrt (fma d d (* c c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 92

Calls

4 calls:

7.0ms	(- (* b c) (* a d))
19.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* b c) (* a d))
182.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
65.0ms	(sqrt (fma d d (* c c)))
52.0ms	(sqrt (fma d d (* c c)))

simplify3.4s

Counts

104 → 104

Iterations

Iter	Nodes
4	5606
3	1999
2	725
1	263
0	112

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.5b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (hypot d c))
27.8b	(sqrt (fma d d (* c c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 179

Calls

4 calls:

13.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
7.0ms	(- (* b c) (* a d))
15.0ms	(/ (- (* b c) (* a d)) (hypot d c))
5.0ms	(sqrt (fma d d (* c c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
50.0ms	(- (* b c) (* a d))
163.0ms	(/ (- (* b c) (* a d)) (hypot d c))
60.0ms	(sqrt (fma d d (* c c)))

simplify1.7s

Counts

191 → 191

Iterations

Iter	Nodes
3	5238
2	1602
1	579
0	252

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot d c))
0.3b	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
0.5b	(- (* c b) (* d a))
16.1b	(/ (- (* c b) (* d a)) (hypot d c))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 139

Calls

4 calls:

8.0ms	(/ 1 (hypot d c))
29.0ms	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
7.0ms	(- (* c b) (* d a))
20.0ms	(/ (- (* c b) (* d a)) (hypot d c))

series469.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1 (hypot d c))
194.0ms	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
48.0ms	(- (* c b) (* d a))
157.0ms	(/ (- (* c b) (* d a)) (hypot d c))

simplify10.1s

Counts

151 → 151

Iterations

Iter	Nodes
3	6273
2	1714
1	502
0	178

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.3b

regimes330.0ms

Accuracy

36.3% (6.4b remaining)

Error of 12.7b against oracle of 6.3b and baseline of 16.3b

bsearch79.0ms

Steps

Iters	Range		Point
8	3.2774015752412573e+161	1.7909529527909587e+165	1.6399786417077545e+162
7	-5.556027931745847e+201	-5.458413144479369e+199	-5.5307531516126024e+200

simplify6.0ms

Iterations

Iter	Nodes
4	32
3	32
2	29
1	26
0	21

end0.0ms

sample1.0s

Algorithm

intervals

Results

825.0ms

8454×

body

valid