Details

sample70.0ms

Algorithm

intervals

Results

33.0ms

264×

body

valid

simplify251.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize121.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(- (* b c) (* a d))
28.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite154.0ms

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`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
29.0ms	(- (* b c) (* a d))
91.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series380.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* c c) (* d d))
89.0ms	(- (* b c) (* a d))
229.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.5s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1114
1	303
0	102

prune889.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.6b

localize152.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
18.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.5b	(sqrt (+ (* c c) (* d d)))
28.5b	(sqrt (+ (* c c) (* d d)))

rewrite180.0ms

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` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

31.0ms	(- (* b c) (* a d))
84.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.0ms	(sqrt (+ (* c c) (* d d)))
28.0ms	(sqrt (+ (* c c) (* d d)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b c) (* a d))
292.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
70.0ms	(sqrt (+ (* c c) (* d d)))
61.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
3	2615
2	902
1	311
0	121

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.9b

localize75.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* d d) (* c c))
0.2b	(- (* b c) (* a d))
28.8b	(/ (- (* b c) (* a d)) (+ (* d d) (* c c)))

rewrite91.0ms

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`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

17.0ms	(+ (* d d) (* c c))
19.0ms	(- (* b c) (* a d))
53.0ms	(/ (- (* b c) (* a d)) (+ (* d d) (* c c)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* d d) (* c c))
60.0ms	(- (* b c) (* a d))
158.0ms	(/ (- (* b c) (* a d)) (+ (* d d) (* c c)))

simplify1.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1113
1	303
0	102

prune657.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.9b

localize88.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* d d) (* c c))
0.2b	(- (* b c) (* a d))
0.3b	(/ 1 (/ (+ (* d d) (* c c)) (- (* b c) (* a d))))
28.7b	(/ (+ (* d d) (* c c)) (- (* b c) (* a d)))

rewrite163.0ms

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×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 142

Calls

4 calls:

18.0ms	(+ (* d d) (* c c))
17.0ms	(- (* b c) (* a d))
51.0ms	(/ 1 (/ (+ (* d d) (* c c)) (- (* b c) (* a d))))
67.0ms	(/ (+ (* d d) (* c c)) (- (* b c) (* a d)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* d d) (* c c))
60.0ms	(- (* b c) (* a d))
184.0ms	(/ 1 (/ (+ (* d d) (* c c)) (- (* b c) (* a d))))
104.0ms	(/ (+ (* d d) (* c c)) (- (* b c) (* a d)))

simplify2.3s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	1647
1	570
0	209

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.9b

regimes843.0ms

Accuracy

-1.5% (3.2b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.4b

bsearch74.0ms

Steps

Iters	Range		Point
4	2.99988769581893e+36	5.314606313626179e+36	5.2422713568197025e+36
8	-7.171553699074835e+91	-1.194776095236265e+88	-7.846283352613039e+90

simplify15.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.2s

Algorithm

intervals

Results

866.0ms

8412×

body

valid