Details

sample29.0ms

Algorithm

intervals

Results

12.0ms

267×

body

valid

simplify54.0ms

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: 28.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* b c) (* a d))
27.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite44.0ms

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:

8.0ms	(- (* b c) (* a d))
34.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series190.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify706.0ms

Counts

50 → 50

Iterations

Useful iterations: done (704.0ms)

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

prune278.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 27.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
18.0b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.1b	(sqrt (+ (* c c) (* d d)))
30.1b	(sqrt (+ (* c c) (* d d)))

rewrite75.0ms

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))
38.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
17.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b c) (* a d))
134.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
44.0ms	(sqrt (+ (* c c) (* d d)))

simplify721.0ms

Counts

98 → 98

Iterations

Useful iterations: done (718.0ms)

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

prune449.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

localize30.0ms

Local error

Found 4 expressions with local error:

18.0b	(/ (- (* b c) (* a d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
30.1b	(sqrt (+ (* c c) (* d d)))
31.0b	(cbrt (+ (* c c) (* d d)))
31.0b	(cbrt (+ (* c c) (* d d)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

33.0ms	(/ (- (* b c) (* a d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
9.0ms	(sqrt (+ (* c c) (* d d)))
5.0ms	(cbrt (+ (* c c) (* d d)))
12.0ms	(cbrt (+ (* c c) (* d d)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

451.0ms	(/ (- (* b c) (* a d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
51.0ms	(sqrt (+ (* c c) (* d d)))
135.0ms	(cbrt (+ (* c c) (* d d)))
131.0ms	(cbrt (+ (* c c) (* d d)))

simplify1.1s

Counts

79 → 79

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	160	1768
1	448	1671
2	2100	1433
done	5000	1427

prune621.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 25.2b

localize31.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
27.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
27.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
27.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

10.0ms	(cbrt (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
44.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
34.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
28.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
126.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
100.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
145.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify723.0ms

Counts

132 → 132

Iterations

Useful iterations: done (714.0ms)

Iter	Nodes	Cost
0	155	3148
1	383	3093
2	1457	2842
done	5000	2826

prune803.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 25.2b

regimes500.0ms

Accuracy

20.5% (2.3b remaining)

Error of 25.2b against oracle of 22.9b and baseline of 25.8b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	53
1	21	53
done	21	53

end0.0ms

sample1.1s

Algorithm

intervals

Results

664.0ms

8517×

body

valid