Details

sample29.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify220.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.4b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite75.0ms

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))
17.0ms	(- (* x x) (* (* y 4.0) y))
40.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* x x) (* (* y 4.0) y))
61.0ms	(- (* x x) (* (* y 4.0) y))
126.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.6s

Counts

76 → 76

Iterations

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

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize0.0ms

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

prune7.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

81×	`prod-diff`
64×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`associate-/r/` `add-cube-cbrt`
24×	`flip3-+` `flip-+`
23×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
9×	`fma-neg`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-out--`
2×	`clear-num` `frac-2neg` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `fma-def` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 182

Calls

4 calls:

8.0ms	(+ (* x x) (* (* y 4.0) y))
85.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
25.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
28.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* x x) (* (* y 4.0) y))
116.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
105.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
85.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify2.7s

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
2	2625
1	758
0	270

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize59.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
13×	`times-frac`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-/r*` `sqrt-prod`
8×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
5×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l*`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 104

Calls

4 calls:

22.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
29.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
29.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
25.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
87.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
91.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
92.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify1.7s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1513
1	383
0	136

prune601.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes199.0ms

Accuracy

62.6% (11.6b remaining)

Error of 12.0b against oracle of 0.4b and baseline of 31.4b

bsearch203.0ms

Steps

Iters	Range		Point
6	1.0558091000171249e+107	1.6495200433389913e+108	1.6131348038947783e+108
5	1.6035341286232548e-95	3.474093194158715e-95	2.0369408682057436e-95
9	-2.6910417602547767e-130	-2.4810864431677805e-136	-2.981255488591297e-134
7	-6.914140684613533e+154	-5.409346264960912e+152	-6.641800154736106e+153

simplify11.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8000×

body

valid