Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

263×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
28.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `sum-log` `fma-def` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 61

Calls

3 calls:

12.0ms	(+ (* c c) (* d d))
13.0ms	(+ (* a c) (* b d))
35.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
42.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify937.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1449
1	304
0	102

prune454.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma d b (* c a)) (hypot c d)))
0.5b	(fma d b (* c a))
18.0b	(/ (fma d b (* c a)) (hypot c d))

rewrite46.0ms

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` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

7.0ms	(/ 1 (hypot c d))
23.0ms	(* (/ 1 (hypot c d)) (/ (fma d b (* c a)) (hypot c d)))
0.0ms	(fma d b (* c a))
4.0ms	(/ (fma d b (* c a)) (hypot c d))

series459.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (hypot c d))
214.0ms	(* (/ 1 (hypot c d)) (/ (fma d b (* c a)) (hypot c d)))
50.0ms	(fma d b (* c a))
131.0ms	(/ (fma d b (* c a)) (hypot c d))

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	3205
1	402
0	154

prune673.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ (/ (fma c a (* d b)) (hypot c d)) (hypot c d))
0.3b	(fma c a (* d b))
18.0b	(/ (fma c a (* d b)) (hypot c d))

rewrite35.0ms

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`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
18.0ms	(/ (/ (fma c a (* d b)) (hypot c d)) (hypot c d))
0.0ms	(fma c a (* d b))
8.0ms	(/ (fma c a (* d b)) (hypot c d))

series402.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(hypot c d)
158.0ms	(/ (/ (fma c a (* d b)) (hypot c d)) (hypot c d))
44.0ms	(fma c a (* d b))
144.0ms	(/ (fma c a (* d b)) (hypot c d))

simplify576.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1787
1	363
0	168

prune676.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ (- (/ (fma d b (* c a)) (hypot c d))) (- (hypot c d)))
0.5b	(fma d b (* c a))
18.0b	(/ (fma d b (* c a)) (hypot c d))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

507×	`times-frac`
270×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
236×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
42×	`neg-mul-1`
33×	`associate-/l*`
24×	`div-inv`
13×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`neg-sub0` `hypot-udef` `div-sub` `distribute-frac-neg` `fma-udef` `distribute-neg-frac` `associate-/l/`

Counts

4 → 406

Calls

4 calls:

0.0ms	(hypot c d)
25.0ms	(/ (- (/ (fma d b (* c a)) (hypot c d))) (- (hypot c d)))
0.0ms	(fma d b (* c a))
4.0ms	(/ (fma d b (* c a)) (hypot c d))

series349.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot c d)
130.0ms	(/ (- (/ (fma d b (* c a)) (hypot c d))) (- (hypot c d)))
46.0ms	(fma d b (* c a))
122.0ms	(/ (fma d b (* c a)) (hypot c d))

simplify484.0ms

Counts

418 → 418

Iterations

Iter	Nodes
done	5000
1	1537
0	606

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

regimes307.0ms

Accuracy

27.2% (10.7b remaining)

Error of 13.2b against oracle of 2.5b and baseline of 17.2b

bsearch85.0ms

Steps

Iters	Range		Point
7	1.786643972454922e+80	1.1640290100133929e+82	1.1461629667173134e+82
8	-1.9950183815385494e+129	-1.3119232040995741e+125	-9.286239316634066e+127

simplify4.0ms

Iterations

Iter	Nodes
done	35
2	35
1	34
0	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

738.0ms

8502×

body

valid