Details

sample42.0ms

Algorithm

intervals

Results

26.0ms

256×

body

valid

simplify242.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	186
7	186
6	177
5	152
4	109
3	67
2	38
1	19
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.4b	(- (* x x) (* (* y 4.0) y))
32.2b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite71.0ms

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×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 67

Calls

3 calls:

16.0ms	(+ (* x x) (* (* y 4.0) y))
16.0ms	(- (* x x) (* (* y 4.0) y))
39.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* x x) (* (* y 4.0) y))
79.0ms	(- (* x x) (* (* y 4.0) y))
89.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4814
2	1023
1	272
0	101

prune337.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune10.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
3.4b	(- (* x x) (* (* y 4.0) y))
32.2b	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `fma-def` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

4 → 153

Calls

4 calls:

16.0ms	(+ (* x x) (* (* y 4.0) y))
39.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
16.0ms	(- (* x x) (* (* y 4.0) y))
61.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* x x) (* (* y 4.0) y))
100.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
66.0ms	(- (* x x) (* (* y 4.0) y))
94.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify1.7s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	1550
1	529
0	209

prune798.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* x x) (* (* y 4.0) y))
30.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

rewrite93.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 100

Calls

4 calls:

20.0ms	(- (* x x) (* (* y 4.0) y))
12.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
14.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
45.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* x x) (* (* y 4.0) y))
120.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
78.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
176.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify3.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4051
2	1002
1	306
0	129

prune592.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes229.0ms

Accuracy

61.6% (12.3b remaining)

Error of 12.6b against oracle of 0.4b and baseline of 32.3b

bsearch213.0ms

Steps

Iters	Range		Point
10	6.851870411809504e+252	2.8918088282269027e+264	3.1031769081973586e+257
10	6.21501595672588e+44	7.598010549864809e+58	6.296502919195928e+44
9	861150181369349.2	2.6348779428485677e+23	9.758857908001147e+18
0	1.4667909825551e-317	1.4216135248906e-313	7.1088010196971e-314

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

932.0ms

8000×

body

valid