Details

sample86.0ms

Algorithm

intervals

Results

17.0ms	30×	body	2560	valid
17.0ms	191×	body	80	valid
9.0ms	18×	body	1280	valid
7.0ms	256×	pre	80	true
4.0ms	10×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	41
5	41
4	40
3	38
2	34
1	27
0	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

77.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(+ (* (* 4.0 p) p) (* x x))
84.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
34.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
65.0ms	(+ (* (* 4.0 p) p) (* x x))
114.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
101.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
2	1079
1	256
0	99

prune488.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
0.6b	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

65.0ms	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
73.0ms	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
11.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
11.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
100.0ms	(+ (/ x (sqrt (+ (* x x) (* (* 4.0 p) p)))) 1.0)
84.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
94.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

simplify2.7s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
4	4322
3	1402
2	466
1	167
0	67

prune524.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.8b

localize80.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* x x) (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

13.0ms	(/ (* x x) (+ (* x x) (* (* 4.0 p) p)))
11.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
9.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
7.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (* x x) (+ (* x x) (* (* 4.0 p) p)))
54.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
60.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
70.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1630
1	229
0	79

prune753.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.8b

localize95.0ms

Local error

Found 4 expressions with local error:

9.9b	(cbrt (* (* (/ (* x x) (+ (* x x) (* (* 4.0 p) p))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))
13.2b	(sqrt (+ (* x x) (* (* 4.0 p) p)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 62

Calls

4 calls:

122.0ms	(cbrt (* (* (/ (* x x) (+ (* x x) (* (* 4.0 p) p))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))))
11.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
12.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
7.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (* (* (/ (* x x) (+ (* x x) (* (* 4.0 p) p))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))) (/ (* x x) (+ (* x x) (* (* 4.0 p) p)))))
79.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
55.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))
56.0ms	(sqrt (+ (* x x) (* (* 4.0 p) p)))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	850
1	180
0	76

prune589.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.8b

regimes449.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample2.3s

Algorithm

intervals

Results

762.0ms	774×	body	2560	valid
459.0ms	6025×	body	80	valid
273.0ms	8000×	pre	80	true
264.0ms	620×	body	1280	valid
103.0ms	268×	body	640	valid
36.0ms	70×	body	5120	valid
33.0ms	166×	body	320	valid
9.0ms	77×	body	160	valid