Details

sample33.0ms

Algorithm

intervals

Results

8.0ms	59×	body	640	valid
6.0ms	154×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	15×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
2	15
1	12
0	7

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
1.6b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 507

Calls

3 calls:

16.0ms	(/ 1.0 (+ x 1.0))
15.0ms	(/ 1.0 (- x 1.0))
190.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ 1.0 (+ x 1.0))
38.0ms	(/ 1.0 (- x 1.0))
242.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify5.6s

Counts

516 → 516

Iterations

Iter	Nodes
done	5002
2	3192
1	1255
0	528

prune2.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (- (fma x (* x 1.0) 1.0) (* x 1.0)) (/ 1.0 (- x 1.0)))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (fma x (* x 1.0) 1.0) (* x 1.0))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
69×	`prod-diff`
65×	`add-cube-cbrt`
61×	`times-frac`
15×	`difference-of-squares`
14×	`distribute-lft-out--`
10×	`add-log-exp`
8×	`associate--l+` `associate-/r/`
7×	`flip3--` `flip--`
6×	`fma-neg`
5×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`diff-log` `div-inv`
3×	`expm1-log1p-u` `pow1` `sub-neg` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`frac-sub` `fma-udef`
1×	`associate--l-` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp`

Counts

3 → 156

Calls

3 calls:

85.0ms	(- (- (fma x (* x 1.0) 1.0) (* x 1.0)) (/ 1.0 (- x 1.0)))
15.0ms	(/ 1.0 (- x 1.0))
10.0ms	(- (fma x (* x 1.0) 1.0) (* x 1.0))

series211.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(- (- (fma x (* x 1.0) 1.0) (* x 1.0)) (/ 1.0 (- x 1.0)))
48.0ms	(/ 1.0 (- x 1.0))
55.0ms	(- (fma x (* x 1.0) 1.0) (* x 1.0))

simplify4.7s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	2340
1	768
0	293

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.3b	(/ 2.0 (* (* x x) (* x x)))
0.5b	(/ 2.0 (* x x))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

226×	`pow1`
72×	`pow-prod-up`
51×	`add-cbrt-cube` `add-exp-log`
46×	`pow-prod-down`
44×	`pow-sqr`
36×	`pow-plus`
26×	`pow2`
25×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-undiv` `div-exp`
6×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 186

Calls

4 calls:

61.0ms	(* (* x x) (* x x))
57.0ms	(* (* x x) (* x x))
63.0ms	(/ 2.0 (* (* x x) (* x x)))
10.0ms	(/ 2.0 (* x x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* x x) (* x x))
61.0ms	(* (* x x) (* x x))
50.0ms	(/ 2.0 (* (* x x) (* x x)))
44.0ms	(/ 2.0 (* x x))

simplify2.7s

Counts

198 → 198

Iterations

Iter	Nodes
done	5019
2	1345
1	313
0	111

prune882.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(/ (/ 2.0 x) x)
0.3b	(/ 2.0 (* (* x x) (* x x)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

226×	`pow1`
78×	`times-frac`
72×	`pow-prod-up`
51×	`add-cbrt-cube` `add-exp-log`
48×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
46×	`pow-prod-down`
44×	`pow-sqr`
36×	`pow-plus`
26×	`pow2`
24×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
8×	`cbrt-undiv` `div-exp`
6×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 235

Calls

4 calls:

38.0ms	(* (* x x) (* x x))
52.0ms	(* (* x x) (* x x))
27.0ms	(/ (/ 2.0 x) x)
57.0ms	(/ 2.0 (* (* x x) (* x x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) (* x x))
61.0ms	(* (* x x) (* x x))
58.0ms	(/ (/ 2.0 x) x)
67.0ms	(/ 2.0 (* (* x x) (* x x)))

simplify3.8s

Counts

247 → 247

Iterations

Iter	Nodes
done	5793
2	1947
1	557
0	216

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes160.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 32.2b

bsearch170.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	1.2575400116675355
10	-26711381.42537418	-6.803810524357175e-07	-1.0026376323582022

simplify30.0ms

Iterations

Iter	Nodes
done	46
3	46
2	42
1	35
0	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

452.0ms	1928×	body	640	valid
280.0ms	1244×	body	320	valid
194.0ms	4192×	body	80	valid
54.0ms	636×	body	160	valid