Details

sample39.0ms

Algorithm

intervals

Results

22.0ms

272×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
26.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite95.0ms

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:

20.0ms	(+ (* c c) (* d d))
16.0ms	(+ (* a c) (* b d))
57.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* c c) (* d d))
66.0ms	(+ (* a c) (* b d))
138.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	3987
2	1000
1	282
0	99

prune412.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
16.8b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite81.0ms

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

Counts

4 → 88

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
46.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* a c) (* b d))
124.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
59.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	2122
2	772
1	281
0	117

prune555.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 24.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
16.9b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

14.0ms	(+ (* a c) (* b d))
73.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
12.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* a c) (* b d))
145.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
49.0ms	(sqrt (+ (* c c) (* d d)))
64.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.7s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
3	3625
2	1216
1	403
0	146

prune611.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 24.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
16.8b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

88.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
57.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
20.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

501.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
148.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
46.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	1906
1	597
0	196

prune632.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 24.1b

regimes333.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample686.0ms

Algorithm

intervals

Results

506.0ms

8467×

body

valid