Details

sample419.0ms

Algorithm

intervals

Results

127.0ms	65×	body	1280	valid
103.0ms	66×	body	10240	exit
72.0ms	51×	body	640	valid
71.0ms	332×	body	80	valid
9.0ms	14×	body	320	valid
4.0ms	9×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
5	3313
4	892
3	314
2	124
1	49
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* x eps) x))
0.0b	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
0.0b	(- (* x eps) x)
4.3b	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
64×	`*-un-lft-identity` `times-frac`
30×	`difference-of-squares`
24×	`add-cube-cbrt`
17×	`exp-sum`
13×	`fma-udef`
11×	`associate-/l*`
10×	`distribute-lft-out--`
9×	`add-log-exp`
6×	`add-cbrt-cube` `prod-diff` `div-inv`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `exp-diff` `fma-neg` `div-sub` `div-exp`

Counts

4 → 128

Calls

4 calls:

19.0ms	(exp (- (* x eps) x))
23.0ms	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
8.0ms	(- (* x eps) x)
0.0ms	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (- (* x eps) x))
28.0ms	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
38.0ms	(- (* x eps) x)
91.0ms	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

simplify1.5s

Counts

140 → 140

Iterations

Iter	Nodes
3	4003
2	1191
1	498
0	238

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (* x x))
6.2b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

19.0ms	(* x (* x x))
1.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series93.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* x (* x x))
45.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify2.8s

Counts

44 → 44

Iterations

Iter	Nodes
4	4942
3	908
2	239
1	103
0	56

prune434.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.4b	(expm1 (log1p (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
6.2b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
11.4b	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt`
5×	`expm1-log1p-u` `*-un-lft-identity` `pow-prod-up` `add-cube-cbrt`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`pow2` `log1p-udef` `expm1-log1p` `pow-plus` `cube-unmult` `associate-r` `log1p-expm1` `pow-sqr` `*-commutative` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

26.0ms	(* x (* x x))
0.0ms	(expm1 (log1p (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
1.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* x (* x x))
141.0ms	(expm1 (log1p (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
34.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
55.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

simplify759.0ms

Counts

74 → 74

Iterations

Iter	Nodes
3	2026
2	637
1	253
0	123

prune855.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize57.0ms

Local error

Found 4 expressions with local error:

6.2b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
6.2b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
11.4b	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))
11.4b	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`expm1-log1p-u`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
1.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))
1.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
59.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
47.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))
83.0ms	(log1p (fma 2/3 (* x (* x x)) (- 2 (* x x))))

simplify1.2s

Counts

58 → 58

Iterations

Iter	Nodes
4	3284
3	797
2	291
1	126
0	63

prune799.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

regimes197.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch358.0ms

Steps

Iters	Range		Point
9	0.08974485042074802	5623247.098758675	307.0243008404694

simplify10.0ms

Iterations

Iter	Nodes
2	36
1	36
0	30

end0.0ms

sample11.2s

Algorithm

intervals

Results

4.5s	2015×	body	10240	exit
2.1s	10189×	body	80	valid
2.1s	1697×	body	1280	valid
1.3s	1316×	body	640	valid
767.0ms	615×	body	320	valid
105.0ms	302×	body	160	valid