Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	51×	body	1280	valid
5.0ms	131×	body	80	valid
5.0ms	39×	body	640	valid
3.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify178.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.5b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `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` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

16.0ms	(/ x (+ x 1))
35.0ms	(/ (+ x 1) (- x 1))
175.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ x (+ x 1))
27.0ms	(/ (+ x 1) (- x 1))
87.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.4s

Counts

762 → 762

Iterations

Iter	Nodes
done	5002
2	3248
1	1369
0	584

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
7.8b	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
33.0b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
54×	`associate-l`
52×	`*-un-lft-identity`
46×	`times-frac`
28×	`add-cube-cbrt`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`pow1` `associate-r` `prod-exp`
6×	`difference-of-sqr-1` `distribute-lft-out--` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 140

Calls

4 calls:

56.0ms	(* (/ 1 (- x 1)) (+ x 1))
48.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ 1 (- x 1)) (+ x 1))
31.0ms	(* (/ 1 (- x 1)) (+ x 1))
105.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
154.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify2.7s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
3	4664
2	1444
1	534
0	157

prune709.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.5b	(expm1 (* (/ 1 (- x 1)) (+ x 1)))
7.8b	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
34.2b	(fma (- (/ 1 (- x 1))) (+ x 1) (log1p (expm1 (* (/ 1 (- x 1)) (+ x 1)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`associate-l`
23×	`times-frac`
16×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `difference-of-squares`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-r` `prod-exp` `insert-posit16` `add-log-exp`
3×	`difference-of-sqr-1` `distribute-lft-out--` `unswap-sqr`
2×	`frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `expm1-log1p` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `flip--` `distribute-lft-out` `expm1-udef`

Counts

4 → 93

Calls

4 calls:

49.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(expm1 (* (/ 1 (- x 1)) (+ x 1)))
0.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (log1p (expm1 (* (/ 1 (- x 1)) (+ x 1)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ 1 (- x 1)) (+ x 1))
73.0ms	(expm1 (* (/ 1 (- x 1)) (+ x 1)))
91.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
819.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (log1p (expm1 (* (/ 1 (- x 1)) (+ x 1)))))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1598
1	602
0	186

prune527.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1))
14.3b	(/ x (- (* x x) (* 1 1)))
29.8b	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
33.0b	(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`times-frac`
7×	`cbrt-prod`
6×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-div` `flip3--` `associate-/r/` `fma-udef` `flip--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/3` `difference-of-sqr-1` `div-exp` `div-inv` `distribute-lft-out--`

Counts

4 → 78

Calls

4 calls:

6.0ms	(cbrt (- x 1))
26.0ms	(/ x (- (* x x) (* 1 1)))
0.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
1.0ms	(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (- x 1))
72.0ms	(/ x (- (* x x) (* 1 1)))
185.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
303.0ms	(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

simplify2.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	4854
2	1383
1	464
0	198

prune926.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.9b

bsearch103.0ms

Steps

Iters	Range		Point
8	29.100869698027953	73049.03827748532	12922.792445976746
9	-343836526097.91516	-3489.5785602046144	-11803.492419360771

simplify20.0ms

Iterations

Iter	Nodes
done	45
2	45
1	40
0	25

end0.0ms

sample1.4s

Algorithm

intervals

Results

612.0ms	1660×	body	1280	valid
313.0ms	1207×	body	640	valid
197.0ms	4154×	body	80	valid
99.0ms	678×	body	320	valid
28.0ms	301×	body	160	valid