Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	47×	body	1280	valid
10.0ms	48×	body	640	valid
7.0ms	131×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	79	13
9	183	13
10	535	13
11	1706	13
12	3584	13
done	5000	13

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 x) (- x 1.0))
2.4b	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub`

Counts

2 → 561

Calls

2 calls:

55.0ms	(/ (+ 1.0 x) (- x 1.0))
251.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series306.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (+ 1.0 x) (- x 1.0))
235.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify3.7s

Counts

567 → 567

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	513	33838
1	1224	30596
2	4492	23162
done	5000	23161

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- x 1.0)) (+ (/ (+ 1.0 x) (- x 1.0)) (/ x (+ x 1.0))))))
0.0b	(pow (/ x (+ x 1.0)) 3)
0.0b	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
2.4b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

5207×	`*-un-lft-identity`
3831×	`times-frac`
3117×	`add-sqr-sqrt`
2498×	`unpow-prod-down` `cube-prod`
2436×	`prod-diff`
2009×	`add-cube-cbrt`
950×	`distribute-lft-out`
609×	`distribute-lft-out--`
524×	`difference-of-squares`
412×	`associate-/r/`
207×	`div-inv`
163×	`sqr-pow`
120×	`flip3-+` `flip-+`
103×	`cube-mult` `unpow3`
88×	`flip3--` `flip--`
77×	`associate-/l*`
42×	`fma-neg`
12×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cube-div` `pow-unpow` `add-log-exp`
5×	`difference-cubes`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
3×	`cbrt-undiv` `div-exp` `associate-/r*` `associate-/l/`
2×	`pow-to-exp` `pow-pow` `frac-sub`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 3028

Calls

4 calls:

1.8s	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- x 1.0)) (+ (/ (+ 1.0 x) (- x 1.0)) (/ x (+ x 1.0))))))
29.0ms	(pow (/ x (+ x 1.0)) 3)
42.0ms	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
722.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- x 1.0)) (+ (/ (+ 1.0 x) (- x 1.0)) (/ x (+ x 1.0))))))
112.0ms	(pow (/ x (+ x 1.0)) 3)
107.0ms	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
509.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ 1.0 x) (- x 1.0)) 3))

simplify2.9s

Counts

3040 → 3040

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	1066	241517
1	2782	208740
done	5004	184616

prune5.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

21.0b	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
21.0b	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
30.4b	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
31.9b	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

140×	`add-sqr-sqrt`
100×	`associate-r`
88×	`*-un-lft-identity`
80×	`unpow-prod-down` `times-frac` `cube-prod`
48×	`add-cube-cbrt` `unswap-sqr`
44×	`add-exp-log`
28×	`associate-l`
24×	`prod-exp` `sqr-pow`
20×	`pow-exp` `distribute-lft-out`
16×	`difference-of-squares`
14×	`cube-div` `pow-to-exp`
8×	`associate-/r/` `add-cbrt-cube`
6×	`div-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `frac-times` `flip3--` `flip3-+` `unpow3` `associate-*l/` `flip--` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 254

Calls

4 calls:

284.0ms	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
275.0ms	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
1.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.0ms	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

series2.2s

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
165.0ms	(* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))
620.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.2s	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

simplify5.9s

Counts

266 → 266

Iterations

Useful iterations: 2 (1.8s)

Iter	Nodes	Cost
0	215	7091
1	626	6733
2	4732	6047
done	5000	6047

prune2.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize176.0ms

Local error

Found 4 expressions with local error:

30.4b	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
30.4b	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
30.4b	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
31.9b	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.0ms	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

series3.2s

Counts

4 → 12

Calls

4 calls:

645.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
639.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
624.0ms	(fma (pow x 3) (pow (/ 1 (+ x 1.0)) 3) (- (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3))))
1.2s	(fma (- (pow (+ x 1.0) 3)) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3) (* (pow (+ x 1.0) 3) (pow (/ (+ 1.0 x) (- (* x x) (* 1.0 1.0))) 3)))

simplify5.2s

Counts

52 → 52

Iterations

Useful iterations: done (5.2s)

Iter	Nodes	Cost
0	61	1853
1	131	1835
2	526	1417
3	4598	1105
done	5000	1102

prune940.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.9b

bsearch323.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	10504.616557362075
10	-906041723027795.1	-3934.6710789005906	-13977.716507512701

simplify31.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	44	211
1	62	196
2	71	196
3	74	196
done	74	196

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1261×	body	640	valid
494.0ms	1749×	body	1280	valid
317.0ms	4049×	body	80	valid
233.0ms	624×	body	320	valid
36.0ms	317×	body	160	valid