Details

sample47.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify262.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	252
7	252
6	244
5	199
4	133
3	77
2	39
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.3b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite43.0ms

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` `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 → 64

Calls

3 calls:

7.0ms	(+ (* x x) (* (* y 4.0) y))
7.0ms	(- (* x x) (* (* y 4.0) y))
27.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(+ (* x x) (* (* y 4.0) y))
92.0ms	(- (* x x) (* (* y 4.0) y))
106.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1796
1	279
0	98

prune450.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

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

prune16.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

3.3b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `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

2 → 48

Calls

2 calls:

13.0ms	(- (* x x) (* (* y 4.0) y))
20.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

series173.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (* x x) (* (* y 4.0) y))
109.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

simplify1.4s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1424
1	241
0	90

prune305.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))))
1.7b	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x))))
3.3b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 70

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))))
0.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x))))
7.0ms	(- (* x x) (* (* y 4.0) y))
31.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(expm1 (log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))))
256.0ms	(log1p (/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x))))
91.0ms	(- (* x x) (* (* y 4.0) y))
121.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma y (* y 4.0) (* x x)))

simplify1.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1505
1	294
0	120

prune436.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes356.0ms

Accuracy

60.4% (12.4b remaining)

Error of 12.8b against oracle of 0.4b and baseline of 31.7b

bsearch214.0ms

Steps

Iters	Range		Point
9	3.0455316621450604e+53	6.601528886642014e+60	2.371593609881423e+60
9	2.598286552721665e-80	1.1482561294715716e-71	9.959621465941043e-80
5	-1.1135581929510197e-64	-2.986264416976082e-65	-3.379561403631359e-65
6	-1.2608308818293039e+154	-1.5171851739610474e+153	-2.0417989825890665e+153

simplify7.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample884.0ms

Algorithm

intervals

Results

582.0ms

8000×

body

valid