Details

sample39.0ms

Algorithm

intervals

Results

28.0ms

272×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
24.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite78.0ms

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×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

10.0ms	(+ (* c c) (* d d))
11.0ms	(+ (* a c) (* b d))
55.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* c c) (* d d))
54.0ms	(+ (* a c) (* b d))
118.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify761.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2004
3	2004
2	1000
1	282
0	99

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

61.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
40.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
160.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
55.0ms	(sqrt (+ (* c c) (* d d)))
53.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.4s

Counts

280 → 280

Iterations

Iter	Nodes
done	2010
3	2010
2	1755
1	724
0	305

prune3.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.0b	(+ (* d d) (* c c))
24.6b	(/ (+ (* a c) (* b d)) (+ (* d d) (* c c)))

rewrite40.0ms

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×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

7.0ms	(+ (* a c) (* b d))
7.0ms	(+ (* d d) (* c c))
26.0ms	(/ (+ (* a c) (* b d)) (+ (* d d) (* c c)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* a c) (* b d))
31.0ms	(+ (* d d) (* c c))
104.0ms	(/ (+ (* a c) (* b d)) (+ (* d d) (* c c)))

simplify1.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
3	2000
2	995
1	282
0	99

prune626.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
24.2b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

13.0ms	(+ (* a c) (* b d))
7.0ms	(+ (* c c) (* d d))
16.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
44.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* a c) (* b d))
43.0ms	(+ (* c c) (* d d))
188.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
81.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify1.2s

Counts

153 → 153

Iterations

Iter	Nodes
done	2000
3	2000
2	1754
1	573
0	208

prune1.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes326.0ms

Accuracy

-0.2% (2.7b remaining)

Error of 26.1b against oracle of 23.4b and baseline of 26.1b

bsearch55.0ms

Steps

Iters	Range		Point
8	-8.814192133652473e+76	-1.2097032068419212e+74	-1.0148544823210362e+76

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

723.0ms

8489×

body

valid