Details

sample52.0ms

Algorithm

intervals

Results

22.0ms

271×

body

valid

simplify95.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.5b	(- (* b c) (* a d))
25.3b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite32.0ms

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))
13.0ms	(- (* b c) (* a d))
16.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(fma d d (* c c))
58.0ms	(- (* b c) (* a d))
160.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1053
1	230
0	95

prune524.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.4b	(/ (- (* 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)))

rewrite40.0ms

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))
25.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
3.0ms	(sqrt (fma d d (* c c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* b c) (* a d))
199.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
82.0ms	(sqrt (fma d d (* c c)))
76.0ms	(sqrt (fma d d (* c c)))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1030
1	264
0	112

prune767.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
0.5b	(- (* b c) (* a d))
16.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
28.7b	(sqrt (fma d d (* c c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `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 → 185

Calls

4 calls:

42.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
8.0ms	(- (* b c) (* a d))
23.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
69.0ms	(- (* b c) (* a d))
205.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
81.0ms	(sqrt (fma d d (* c c)))

simplify1.7s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	2768
1	620
0	253

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.5b	(- (* b c) (* a d))
16.4b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot d c)
16.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
7.0ms	(- (* b c) (* a d))
16.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series423.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot d c)
159.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
49.0ms	(- (* b c) (* a d))
155.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.3s

Counts

143 → 143

Iterations

Iter	Nodes
done	5002
2	2290
1	483
0	192

prune854.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

regimes419.0ms

Accuracy

28.7% (8.3b remaining)

Error of 13.4b against oracle of 5.0b and baseline of 16.7b

bsearch111.0ms

Steps

Iters	Range		Point
10	1.5425824365857962e+73	1.5192017912580791e+85	2.805404912411876e+84
8	-3.35691658268957e+164	-1.5338344244864082e+161	-8.30562369060115e+163

simplify8.0ms

Iterations

Iter	Nodes
done	27
2	27
1	25
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

977.0ms

8499×

body

valid