Details

sample56.0ms

Algorithm

intervals

Results

30.0ms

271×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	72
5	72
4	66
3	48
2	36
1	19
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
30.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite55.0ms

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))
11.0ms	(- (* b c) (* a d))
36.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* c c) (* d d))
60.0ms	(- (* b c) (* a d))
119.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1712
1	315
0	99

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
17.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
33.8b	(sqrt (+ (* c c) (* d d)))
33.8b	(sqrt (+ (* c c) (* d d)))

rewrite59.0ms

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`
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 → 86

Calls

4 calls:

6.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
15.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* b c) (* a d))
196.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1128
1	308
0	118

prune575.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 28.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
0.7b	(/ 1 (+ (* c c) (* d d)))
30.2b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `flip3-+` `flip3--` `associate-l` `flip-+` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 98

Calls

4 calls:

7.0ms	(+ (* c c) (* d d))
15.0ms	(- (* b c) (* a d))
12.0ms	(/ 1 (+ (* c c) (* d d)))
55.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* c c) (* d d))
62.0ms	(- (* b c) (* a d))
42.0ms	(/ 1 (+ (* c c) (* d d)))
113.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify2.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	3313
1	417
0	138

prune547.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 28.4b

localize41.0ms

Local error

Found 4 expressions with local error:

17.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
33.8b	(sqrt (+ (* c c) (* d d)))
34.9b	(cbrt (+ (* c c) (* d d)))
34.9b	(cbrt (+ (* c c) (* d d)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`cbrt-prod` `associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 85

Calls

4 calls:

31.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
110.0ms	(cbrt (+ (* c c) (* d d)))
128.0ms	(cbrt (+ (* c c) (* d d)))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1289
1	335
0	135

prune689.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 28.4b

regimes550.0ms

Accuracy

0% (3.2b remaining)

Error of 26.9b against oracle of 23.7b and baseline of 26.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample830.0ms

Algorithm

intervals

Results

576.0ms

8480×

body

valid