Details

sample50.0ms

Algorithm

intervals

Results

34.0ms

256×

body

valid

simplify262.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	215
7	215
6	209
5	182
4	128
3	77
2	39
1	19
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize44.0ms

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)))

rewrite51.0ms

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:

9.0ms	(+ (* x x) (* (* y 4.0) y))
9.0ms	(- (* x x) (* (* y 4.0) y))
32.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (* x x) (* (* y 4.0) y))
55.0ms	(- (* x x) (* (* y 4.0) y))
103.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4944
2	1042
1	272
0	101

prune413.0ms

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

prune14.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize58.0ms

Local error

Found 4 expressions with local error:

19.0b	(/ (fma y (* y 4.0) (* x x)) (* y 4.0))
22.5b	(/ (* x x) (fma y (* y 4.0) (* x x)))
22.5b	(/ (* x x) (fma y (* y 4.0) (* x x)))
22.5b	(/ (* x x) (fma y (* y 4.0) (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
10×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 96

Calls

4 calls:

7.0ms	(/ (fma y (* y 4.0) (* x x)) (* y 4.0))
15.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))
16.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))
21.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (fma y (* y 4.0) (* x x)) (* y 4.0))
75.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))
67.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))
59.0ms	(/ (* x x) (fma y (* y 4.0) (* x x)))

simplify2.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5102
3	3653
2	816
1	238
0	95

prune615.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize47.0ms

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))))

rewrite73.0ms

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:

16.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
11.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
31.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* x x) (* (* y 4.0) y))
83.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
87.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
150.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify2.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4038
2	1016
1	306
0	129

prune611.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes272.0ms

Accuracy

62.3% (12.1b remaining)

Error of 12.4b against oracle of 0.4b and baseline of 32.3b

bsearch231.0ms

Steps

Iters	Range		Point
7	4.517066370264425e+293	2.571276409140139e+295	2.524624859163763e+295
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

simplify15.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample1.0s

Algorithm

intervals

Results

797.0ms

8000×

body

valid