Details

sample76.0ms

Algorithm

intervals

Results

24.0ms	53×	body	640	valid
16.0ms	137×	body	80	valid
12.0ms	34×	body	320	valid
10.0ms	19×	body	1280	valid
3.0ms	13×	body	160	valid

simplify247.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	475
9	475
8	357
7	164
6	102
5	81
4	65
3	45
2	35
1	21
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))
2.7b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

17.0ms	(/ 1 (- x 1))
50.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms	(/ 1 (+ x 1))
174.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
42.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
24.0ms	(/ 1 (+ x 1))
163.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.8s

Counts

660 → 660

Iterations

Iter	Nodes
done	5000
2	2961
1	1148
0	495

prune2.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (/ 2 x) (/ 1 (+ x 1)))
0.1b	(+ (/ 2 x) (/ 1 (+ x 1)))
6.6b	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
15.3b	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (+ (/ 2 x) (/ 1 (+ x 1)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
29×	`times-frac`
26×	`fma-def`
20×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`associate-/r/`
10×	`distribute-lft-out`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`frac-times`
5×	`flip3-+` `frac-add` `flip-+` `div-inv`
4×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-r/` `associate-/l`
2×	`cbrt-undiv` `+-commutative` `sum-log` `div-exp` `associate-*l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`

Counts

4 → 110

Calls

4 calls:

35.0ms	(+ (/ 2 x) (/ 1 (+ x 1)))
33.0ms	(+ (/ 2 x) (/ 1 (+ x 1)))
0.0ms	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
52.0ms	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (+ (/ 2 x) (/ 1 (+ x 1)))))

series912.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (/ 2 x) (/ 1 (+ x 1)))
35.0ms	(+ (/ 2 x) (/ 1 (+ x 1)))
267.0ms	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
579.0ms	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (+ (/ 2 x) (/ 1 (+ x 1)))))

simplify2.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5026
2	2166
1	474
0	157

prune647.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma (* x x) x (/ 1 x)) x)
0.1b	(fma (* x x) x (/ 1 x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 30

Calls

2 calls:

10.0ms	(+ (fma (* x x) x (/ 1 x)) x)
1.0ms	(fma (* x x) x (/ 1 x))

series178.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+ (fma (* x x) x (/ 1 x)) x)
127.0ms	(fma (* x x) x (/ 1 x))

simplify1.4s

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
3	1273
2	304
1	91
0	41

prune155.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
6.6b	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
15.3b	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (fma (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (/ (cbrt 2) (cbrt x)) (/ 1 (+ x 1)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow1/3` `div-exp` `associate-*l/` `associate-/r/`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3--` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `flip--`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
0.0ms	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
10.0ms	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (fma (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (/ (cbrt 2) (cbrt x)) (/ 1 (+ x 1)))))

series814.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
230.0ms	(fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1))))
583.0ms	(/ (fma (+ (/ 2 x) (/ 1 (+ x 1))) (* (+ (/ 1 (+ x 1)) (/ -2 x)) (- x 1)) (+ (/ 2 x) (/ 1 (+ x 1)))) (* (- x 1) (fma (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (/ (cbrt 2) (cbrt x)) (/ 1 (+ x 1)))))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1473
1	390
0	158

prune894.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes119.0ms

Accuracy

96.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 10.2b

bsearch2.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample2.3s

Algorithm

intervals

Results

845.0ms	1890×	body	640	valid
545.0ms	4153×	body	80	valid
377.0ms	936×	body	320	valid
308.0ms	557×	body	1280	valid
140.0ms	467×	body	160	valid