Details

sample55.0ms

Algorithm

intervals

Results

31.0ms

267×

body

valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* b c) (* a d))
25.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

17.0ms	(- (* b c) (* a d))
63.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (* b c) (* a d))
136.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify833.0ms

Counts

50 → 50

Iterations

Useful iterations: done (831.0ms)

Iter	Nodes	Cost
0	88	954
1	258	936
2	1076	856
done	5000	854

prune237.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
16.2b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
46.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b c) (* a d))
146.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
55.0ms	(sqrt (+ (* c c) (* d d)))
46.0ms	(sqrt (+ (* c c) (* d d)))

simplify931.0ms

Counts

98 → 98

Iterations

Useful iterations: done (921.0ms)

Iter	Nodes	Cost
0	120	1814
1	312	1682
2	1189	1576
done	5000	1574

prune422.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize28.0ms

Local error

Found 3 expressions with local error:

0.3b	(- (* b c) (* a d))
0.8b	(/ 1 (+ (* c c) (* d d)))
24.6b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

8.0ms	(- (* b c) (* a d))
14.0ms	(/ 1 (+ (* c c) (* d d)))
82.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series246.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- (* b c) (* a d))
47.0ms	(/ 1 (+ (* c c) (* d d)))
128.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify3.1s

Counts

96 → 96

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	127	1631
1	365	1521
2	2531	1308
done	5001	1302

prune306.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.4b

localize28.0ms

Local error

Found 4 expressions with local error:

11.6b	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 101

Calls

4 calls:

44.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
52.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))
48.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: 3 (834.0ms)

Iter	Nodes	Cost
0	144	2355
1	339	2146
2	1181	2030
3	4837	2006
done	5002	2006

prune401.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.4b

regimes128.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
done	16	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

796.0ms

8438×

body

valid