Details

sample102.0ms

Algorithm

intervals

Results

19.0ms	197×	body	80	valid
17.0ms	19×	body	2560	valid
12.0ms	23×	body	1280	valid
8.0ms	256×	pre	80	true
3.0ms	7×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify140.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	40
4	40
3	38
2	34
1	27
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

98.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
113.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
69.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series752.0ms

Counts

3 → 9

Calls

3 calls:

505.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
161.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
85.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify6.9s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
4	3325
3	1412
2	548
1	211
0	91

prune736.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite953.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`pow1`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`log-pow`
4×	`log-prod` `exp-prod` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
3×	`sqrt-pow1`
2×	`flip3-+` `pow1/2` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-log-exp` `exp-sum` `pow-prod-down`

Counts

4 → 59

Calls

4 calls:

379.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
95.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
423.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series907.0ms

Counts

4 → 12

Calls

4 calls:

498.0ms	(sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
163.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
166.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
80.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify6.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
4	2918
3	1350
2	560
1	231
0	109

prune981.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize208.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
13×	`sqrt-prod`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1/3` `sqrt-div` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

32.0ms	(* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
42.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
43.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

990.0ms	(* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
86.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
108.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
91.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify7.0s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
4	4809
3	1558
2	623
1	251
0	116

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize217.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (exp (* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
5×	`add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `log-prod` `sqrt-pow1` `flip3-+` `pow1/2` `log-pow` `flip-+`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 63

Calls

4 calls:

5.0ms	(log (exp (* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))))
32.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
35.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
37.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(log (exp (* (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))) (cbrt (sqrt (* 0.5 (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))))
106.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
89.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
109.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify4.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5024
4	3780
3	1196
2	455
1	190
0	91

prune878.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

regimes1.2s

Accuracy

78.7% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 14.4b

bsearch4.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	43
1	43
0	34

end0.0ms

sample1.9s

Algorithm

intervals

Results

631.0ms	744×	body	2560	valid
418.0ms	6027×	body	80	valid
200.0ms	8000×	pre	80	true
171.0ms	599×	body	1280	valid
134.0ms	324×	body	640	valid
57.0ms	172×	body	320	valid
26.0ms	58×	body	5120	valid
8.0ms	76×	body	160	valid