Details

sample65.0ms

Algorithm

intervals

Results

21.0ms	48×	body	1280	valid
12.0ms	34×	body	640	valid
12.0ms	131×	body	80	valid
8.0ms	28×	body	320	valid
3.0ms	15×	body	160	valid

simplify162.0ms

Counts

1 → 1

Iterations

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
4.4b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite132.0ms

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:

12.0ms	(/ x (+ x 1))
20.0ms	(/ (+ x 1) (- x 1))
69.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ x (+ x 1))
33.0ms	(/ (+ x 1) (- x 1))
83.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.5s

Counts

762 → 762

Iterations

Iter	Nodes
2	3080
1	1349
0	584

prune7.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
29.5b	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
32.3b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite89.0ms

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:

51.0ms	(* (/ 1 (- x 1)) (+ x 1))
33.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ 1 (- x 1)) (+ x 1))
43.0ms	(* (/ 1 (- x 1)) (+ x 1))
95.0ms	(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
152.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify3.6s

Counts

152 → 152

Iterations

Iter	Nodes
3	3505
2	1231
1	513
0	157

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
4.3b	(/ x (fma (* x x) x 1))
14.7b	(* (/ x (fma (* x x) x 1)) (- (fma x x 1) x))
21.6b	(- (* (/ x (fma (* x x) x 1)) (- (fma x x 1) x)) (/ (* (cbrt (+ 1 x)) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (- x 1)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt` `*-un-lft-identity`
54×	`add-cube-cbrt`
49×	`prod-diff`
28×	`associate--l+`
26×	`times-frac`
24×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in`
20×	`associate-l`
13×	`pow1` `add-exp-log`
12×	`cbrt-div` `associate-r`
11×	`add-cbrt-cube`
9×	`swap-sqr`
8×	`frac-times`
6×	`flip3-+` `flip3--` `pow1/3` `associate-*r/` `flip-+` `flip--` `distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`sub-neg` `frac-sub`
4×	`expm1-log1p-u` `associate-*l/` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l` `difference-of-squares`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `distribute-lft-out--`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `difference-of-sqr-1`

Counts

4 → 209

Calls

4 calls:

27.0ms	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
4.0ms	(/ x (fma (* x x) x 1))
25.0ms	(* (/ x (fma (* x x) x 1)) (- (fma x x 1) x))
25.0ms	(- (* (/ x (fma (* x x) x 1)) (- (fma x x 1) x)) (/ (* (cbrt (+ 1 x)) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (- x 1)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
156.0ms	(/ x (fma (* x x) x 1))
112.0ms	(* (/ x (fma (* x x) x 1)) (- (fma x x 1) x))
222.0ms	(- (* (/ x (fma (* x x) x 1)) (- (fma x x 1) x)) (/ (* (cbrt (+ 1 x)) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (- x 1)))

simplify2.7s

Counts

221 → 221

Iterations

Iter	Nodes
2	3733
1	1114
0	421

prune3.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
14.6b	(/ (fma x x -1) (* (- x 1) (- x 1)))
29.5b	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
32.3b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`associate-l`
26×	`times-frac`
18×	`add-exp-log` `add-cube-cbrt`
14×	`add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`frac-times` `pow1` `difference-of-squares`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `associate-r` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `difference-of-sqr-1` `associate-l/` `cbrt-unprod` `associate-/l` `distribute-lft-out--` `unswap-sqr`
2×	`flip3-+` `flip-+` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `rec-exp` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `1-exp` `pow-prod-down` `-commutative` `distribute-lft-out`

Counts

4 → 113

Calls

4 calls:

32.0ms	(* (/ 1 (- x 1)) (+ x 1))
27.0ms	(/ (fma x x -1) (* (- x 1) (- x 1)))
1.0ms	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
1.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ 1 (- x 1)) (+ x 1))
59.0ms	(/ (fma x x -1) (* (- x 1) (- x 1)))
114.0ms	(fma x (/ 1 (+ x 1)) (- (/ (fma x x -1) (* (- x 1) (- x 1)))))
188.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify17.0s

Counts

125 → 125

Iterations

Iter	Nodes
3	7343
2	1760
1	621
0	212

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.1b

bsearch138.0ms

Steps

Iters	Range		Point
10	186.95626557948964	3373396396890550.5	12311.34325898398
9	-24078.920296370652	-0.35383103211093586	-13167.552073147652

simplify7.0ms

Iterations

Iter	Nodes
2	43
1	43
0	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	1698×	body	1280	valid
494.0ms	1267×	body	640	valid
372.0ms	4118×	body	80	valid
195.0ms	626×	body	320	valid
50.0ms	291×	body	160	valid

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7

Iter	Nodes
17	206
16	206
15	204
14	192
13	143
12	112
11	99
10	90
9	68
8	51
7	40
6	30
5	24
4	21
3	20
2	17
1	13
0	7