Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify263.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.6b

localize15.0ms

Local error

Found 2 expressions with local error:

1.3b	(fma (* y 4.0) (- y) (* x x))
30.1b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

rewrite6.0ms

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`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (* y 4.0) (- y) (* x x))
4.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

series254.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(fma (* y 4.0) (- y) (* x x))
167.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

simplify1.4s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	2061
2	344
1	118
0	67

prune318.0ms

Pruning

5 alts after pruning (4 fresh and 1 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

prune18.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `log1p-udef` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `div-inv`

Counts

4 → 60

Calls

4 calls:

0.0ms	(fma x x (* y (* 4.0 y)))
1.0ms	(log1p (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))))
0.0ms	(fma 4.0 (* y (- y)) (* x x))
11.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma x x (* y (* 4.0 y)))
269.0ms	(log1p (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))))
74.0ms	(fma 4.0 (* y (- y)) (* x x))
98.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2710
2	493
1	184
0	103

prune494.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))))
0.5b	(expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))))
3.3b	(fma 4.0 (* y (- y)) (* x x))
30.1b	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

rewrite9.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `fma-udef` `div-inv` `expm1-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))))
1.0ms	(expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))))
1.0ms	(fma 4.0 (* y (- y)) (* x x))
5.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(log1p (expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))))
190.0ms	(expm1 (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))))
92.0ms	(fma 4.0 (* y (- y)) (* x x))
117.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	2110
2	403
1	157
0	92

prune494.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.4b

regimes318.0ms

Accuracy

60.4% (12.4b remaining)

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

bsearch187.0ms

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

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample909.0ms

Algorithm

intervals

Results

615.0ms

8000×

body

valid