Details

sample44.0ms

Algorithm

intervals

Results

22.0ms

274×

body

valid

simplify69.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `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

2 → 48

Calls

2 calls:

18.0ms	(- (* b c) (* a d))
28.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series220.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (* b c) (* a d))
147.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify2.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	3648
2	798
1	218
0	86

prune359.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
28.7b	(sqrt (fma d d (* c c)))
28.7b	(sqrt (fma d d (* c c)))

rewrite27.0ms

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:

6.0ms	(- (* b c) (* a d))
16.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b c) (* a d))
216.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
51.0ms	(sqrt (fma d d (* c c)))
62.0ms	(sqrt (fma d d (* c c)))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1030
1	264
0	112

prune805.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize39.0ms

Local error

Found 3 expressions with local error:

0.5b	(- (* b c) (* a d))
1.3b	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
23.8b	(/ (fma d d (* c c)) (- (* b c) (* a d)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

3 → 133

Calls

3 calls:

6.0ms	(- (* b c) (* a d))
23.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
19.0ms	(/ (fma d d (* c c)) (- (* b c) (* a d)))

series372.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(- (* b c) (* a d))
195.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
114.0ms	(/ (fma d d (* c c)) (- (* b c) (* a d)))

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5002
2	2505
1	480
0	194

prune825.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
0.5b	(- (* c b) (* d a))
15.4b	(/ (- (* c b) (* d a)) (hypot d c))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `add-exp-log`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 106

Calls

3 calls:

37.0ms	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
9.0ms	(- (* c b) (* d a))
14.0ms	(/ (- (* c b) (* d a)) (hypot d c))

series420.0ms

Counts

3 → 9

Calls

3 calls:

218.0ms	(* (/ 1 (hypot d c)) (/ (- (* c b) (* d a)) (hypot d c)))
54.0ms	(- (* c b) (* d a))
147.0ms	(/ (- (* c b) (* d a)) (hypot d c))

simplify1.7s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2498
1	489
0	164

prune668.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

regimes453.0ms

Accuracy

30.9% (7.7b remaining)

Error of 13.4b against oracle of 5.6b and baseline of 16.8b

bsearch71.0ms

Steps

Iters	Range		Point
6	9.626016829055456e+181	6.57262008803295e+182	1.1505677994297552e+182
8	-2.918334147983184e+213	-9.208215021773174e+210	-9.293826114497671e+210

simplify7.0ms

Iterations

Iter	Nodes
done	34
3	34
2	31
1	28
0	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

966.0ms

8465×

body

valid