Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	51×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	202
1	12	202
2	16	202
3	19	202
4	21	202
5	27	202
6	39	202
7	58	202
8	79	202
9	183	202
10	535	202
11	1745	202
12	4085	202
done	5000	202

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

11.0ms	(/ x (+ x 1.0))
30.0ms	(/ (+ x 1.0) (- x 1.0))
154.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series313.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ x (+ x 1.0))
64.0ms	(/ (+ x 1.0) (- x 1.0))
197.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.6s

Counts

605 → 605

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	523	485239
1	1252	423577
2	4599	377618
done	5000	377568

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
29.5b	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
49×	`times-frac`
34×	`add-cube-cbrt`
21×	`associate-l`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`distribute-lft-out`
9×	`associate-/r*`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/l*`
6×	`associate-/r/`
5×	`div-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `prod-exp` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `flip3--` `1-exp` `associate-*r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 148

Calls

4 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
24.0ms	(/ 1 (+ x 1.0))
69.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ x 1.0) (- x 1.0))
27.0ms	(/ 1 (+ x 1.0))
67.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
212.0ms	(fma x (/ 1 (+ x 1.0)) (- (* (/ 1 (- x 1.0)) (+ x 1.0))))

simplify887.0ms

Counts

160 → 160

Iterations

Useful iterations: done (863.0ms)

Iter	Nodes	Cost
0	227	43757
1	654	35391
done	5000	31835

prune799.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
0.5b	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
29.5b	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`associate-l`
17×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-r` `prod-exp` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `log1p-udef` `expm1-log1p` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log1p-expm1` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out` `expm1-udef`

Counts

4 → 84

Calls

4 calls:

0.0ms	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
56.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
1.0ms	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

series898.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))
67.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
170.0ms	(expm1 (* (/ 1 (- x 1.0)) (+ x 1.0)))
431.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ 1 (- x 1.0)) (+ x 1.0))))))

simplify2.7s

Counts

96 → 96

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	181	31664
1	565	23660
2	3894	19786
done	5000	19528

prune504.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))
0.1b	(/ (sqrt (+ x 1.0)) (- x 1.0))
0.3b	(expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0))))
15.7b	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
74×	`times-frac`
53×	`sqrt-prod`
44×	`add-cube-cbrt`
41×	`associate-l`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
7×	`associate-r` `associate-/l*`
6×	`pow1` `sqrt-div` `unswap-sqr`
5×	`associate-/r*` `log1p-expm1-u`
4×	`expm1-log1p-u` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-times` `cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `flip--` `associate-/l/`
1×	`expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `expm1-udef`

Counts

4 → 160

Calls

4 calls:

68.0ms	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))
32.0ms	(/ (sqrt (+ x 1.0)) (- x 1.0))
1.0ms	(expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0))))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))
162.0ms	(/ (sqrt (+ x 1.0)) (- x 1.0))
115.0ms	(expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0))))
409.0ms	(fma x (/ 1 (+ x 1.0)) (- (log1p (expm1 (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (sqrt (+ x 1.0)))))))

simplify2.6s

Counts

172 → 172

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	243	62092
1	611	54054
2	2761	48334
done	5000	47843

prune891.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.8b

bsearch144.0ms

Steps

Iters	Range		Point
8	160.65039477392645	261980.93535209994	9776.98433563854
10	-83422883652835.42	-0.9341403346610884	-0.9906799218317324

simplify25.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	32	1202
1	44	1202
done	44	1202

end0.0ms

sample1.8s

Algorithm

intervals

Results

670.0ms	4096×	body	80	valid
518.0ms	1667×	body	1280	valid
282.0ms	1320×	body	640	valid
89.0ms	587×	body	320	valid
31.0ms	330×	body	160	valid