Details

sample29.0ms

Algorithm

intervals

Results

12.0ms

283×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* b d) (* a c))
24.7b	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

6.0ms	(+ (* b d) (* a c))
34.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(+ (* b d) (* a c))
148.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

simplify2.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	4324
2	904
1	235
0	84

prune374.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite166.0ms

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` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 264

Calls

4 calls:

67.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
49.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
13.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
141.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
55.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
2	3738
1	755
0	302

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
14.7b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

25.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
25.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
113.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
60.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts

205 → 205

Iterations

Iter	Nodes
done	5001
2	3631
1	642
0	242

prune810.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

7.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+ (* a c) (* b d))
109.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	4513
2	925
1	235
0	83

prune231.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.5b

regimes588.0ms

Accuracy

0% (2.8b remaining)

Error of 25.8b against oracle of 23.0b and baseline of 25.8b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample955.0ms

Algorithm

intervals

Results

575.0ms

8478×

body

valid