Details

sample35.0ms

Algorithm

intervals

Results

17.0ms

272×

body

valid

simplify40.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(- (* b c) (* a d))
27.7b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite33.0ms

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` `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 → 55

Calls

3 calls:

6.0ms	(+ (* c c) (* d d))
6.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
55.0ms	(- (* b c) (* a d))
101.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5113
3	4064
2	1053
1	300
0	99

prune443.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
17.2b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite100.0ms

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*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`flip3--` `flip--`

Counts

4 → 266

Calls

4 calls:

49.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
20.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
140.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
52.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.8s

Counts

278 → 278

Iterations

Iter	Nodes
done	5000
2	2095
1	741
0	307

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.3b

localize30.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ a (/ (+ (* c c) (* d d)) d))
7.9b	(/ (+ (* c c) (* d d)) b)
12.4b	(/ c (/ (+ (* c c) (* d d)) b))
18.4b	(/ (+ (* c c) (* d d)) d)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
104×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
12×	`div-inv` `associate-/l*`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp` `associate-/l/`
2×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 198

Calls

4 calls:

13.0ms	(/ a (/ (+ (* c c) (* d d)) d))
18.0ms	(/ (+ (* c c) (* d d)) b)
11.0ms	(/ c (/ (+ (* c c) (* d d)) b))
19.0ms	(/ (+ (* c c) (* d d)) d)

series230.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ a (/ (+ (* c c) (* d d)) d))
49.0ms	(/ (+ (* c c) (* d d)) b)
80.0ms	(/ c (/ (+ (* c c) (* d d)) b))
50.0ms	(/ (+ (* c c) (* d d)) d)

simplify1.3s

Counts

210 → 210

Iterations

Iter	Nodes
done	5000
2	2680
1	818
0	314

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.8b

localize30.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ a (+ d (/ (* c c) d)))
6.0b	(/ (* c c) d)
7.9b	(/ (+ (* c c) (* d d)) b)
12.4b	(/ c (/ (+ (* c c) (* d d)) b))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
73×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
8×	`div-inv`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `distribute-lft-out` `add-log-exp`
3×	`associate-/r/`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 153

Calls

4 calls:

12.0ms	(/ a (+ d (/ (* c c) d)))
7.0ms	(/ (* c c) d)
18.0ms	(/ (+ (* c c) (* d d)) b)
11.0ms	(/ c (/ (+ (* c c) (* d d)) b))

series183.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ a (+ d (/ (* c c) d)))
20.0ms	(/ (* c c) d)
50.0ms	(/ (+ (* c c) (* d d)) b)
78.0ms	(/ c (/ (+ (* c c) (* d d)) b))

simplify1.1s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	2282
1	674
0	261

prune688.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

regimes259.0ms

Accuracy

0% (4.2b remaining)

Error of 15.8b against oracle of 11.6b and baseline of 15.8b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample971.0ms

Algorithm

intervals

Results

742.0ms

8484×

body

valid