Details

sample37.0ms

Algorithm

intervals

Results

26.0ms

267×

body

valid

simplify44.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
24.1b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite51.0ms

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:

14.0ms	(+ (* c c) (* d d))
8.0ms	(- (* b c) (* a d))
28.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* c c) (* d d))
79.0ms	(- (* b c) (* a d))
108.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify549.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2002
2	1065
1	303
0	102

prune400.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
15.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.0b	(sqrt (+ (* c c) (* d d)))
31.0b	(sqrt (+ (* c c) (* d d)))

rewrite51.0ms

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:

9.0ms	(- (* b c) (* a d))
24.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b c) (* a d))
170.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
52.0ms	(sqrt (+ (* c c) (* d d)))
73.0ms	(sqrt (+ (* c c) (* d d)))

simplify734.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
2	897
1	311
0	121

prune650.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.0b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
31.0b	(sqrt (+ (* c c) (* d d)))
31.0b	(sqrt (+ (* c c) (* d d)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r*` `flip3-+` `flip-+`
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-exp` `div-inv`

Counts

4 → 89

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
21.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b c) (* a d))
113.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify917.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	2002
3	1847
2	717
1	271
0	116

prune565.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.4b

localize67.0ms

Local error

Found 4 expressions with local error:

8.2b	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))
31.0b	(sqrt (+ (* c c) (* d d)))
31.0b	(sqrt (+ (* c c) (* d d)))
31.0b	(sqrt (+ (* c c) (* d d)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
108×	`sqrt-prod`
99×	`times-frac`
57×	`*-un-lft-identity`
45×	`add-cube-cbrt`
33×	`associate-r` `associate-l`
28×	`unswap-sqr`
26×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`sqrt-div`
9×	`pow1`
8×	`div-exp` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 167

Calls

4 calls:

94.0ms	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))
6.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))))
64.0ms	(sqrt (+ (* c c) (* d d)))
50.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts

179 → 179

Iterations

Iter	Nodes
done	2000
2	1797
1	603
0	201

prune871.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.4b

regimes516.0ms

Accuracy

0% (2.7b remaining)

Error of 25.9b against oracle of 23.2b and baseline of 25.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8493×

body

valid