Details

sample64.0ms

Algorithm

intervals

Results

26.0ms	50×	body	1280	valid
11.0ms	137×	body	80	valid
10.0ms	33×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify152.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
4.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite151.0ms

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))
29.0ms	(/ (+ x 1) (- x 1))
82.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ x (+ x 1))
25.0ms	(/ (+ x 1) (- x 1))
85.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.6s

Counts

762 → 762

Iterations

Iter	Nodes
done	5002
2	3248
1	1369
0	584

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
0.0b	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
4.1b	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

444×	`*-un-lft-identity`
281×	`times-frac`
276×	`add-sqr-sqrt`
135×	`add-cube-cbrt`
81×	`distribute-lft-out`
72×	`swap-sqr` `prod-diff`
64×	`difference-of-squares`
38×	`distribute-lft-out--`
37×	`difference-of-sqr-1`
34×	`associate-r` `associate-l`
20×	`associate-/r/`
19×	`cbrt-prod`
18×	`add-cbrt-cube` `fma-neg` `add-exp-log`
14×	`cbrt-div`
11×	`frac-times` `pow1` `associate-*l/`
10×	`div-inv`
7×	`associate-/r` `associate-r/` `frac-sub`
6×	`flip3-+` `flip3--` `flip-+` `flip--` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
2×	`associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `pow1/3` `diff-log` `pow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 364

Calls

4 calls:

18.0ms	(/ (+ x 1) (- x 1))
78.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
58.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
68.0ms	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ x 1) (- x 1))
64.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
50.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
111.0ms	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

simplify2.9s

Counts

376 → 376

Iterations

Iter	Nodes
done	5002
2	3896
1	1205
0	403

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1)))
0.3b	(cbrt (- x 1))
0.3b	(cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1))))
4.1b	(- (/ x (+ x 1)) (/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

1335×	`times-frac`
1271×	`*-un-lft-identity`
1075×	`add-sqr-sqrt`
828×	`prod-diff`
744×	`add-cube-cbrt`
740×	`cbrt-prod`
162×	`difference-of-squares`
142×	`distribute-lft-out`
132×	`associate-/r/`
81×	`distribute-lft-out--`
78×	`difference-of-sqr-1`
66×	`div-inv`
62×	`cbrt-div`
55×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`frac-times` `fma-neg`
14×	`associate-*l/`
11×	`associate-/l/`
10×	`associate-/r` `associate-r/`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow1/3`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`

Counts

4 → 996

Calls

4 calls:

19.0ms	(/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1)))
4.0ms	(cbrt (- x 1))
54.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1))))
77.0ms	(- (/ x (+ x 1)) (/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1)))
67.0ms	(cbrt (- x 1))
82.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1))))
173.0ms	(- (/ x (+ x 1)) (/ (cbrt (* (* (/ (+ x 1) (- x 1)) (+ x 1)) (/ (+ x 1) (- x 1)))) (cbrt (- x 1))))

simplify2.7s

Counts

1008 → 1008

Iterations

Iter	Nodes
done	5000
1	2441
0	1047

prune5.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.1b	(/ x (sqrt (+ x 1)))
12.5b	(fma (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
32.1b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `pow-flip`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+` `fma-udef` `div-inv`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 124

Calls

4 calls:

9.0ms	(/ 1 (sqrt (+ x 1)))
9.0ms	(/ x (sqrt (+ x 1)))
0.0ms	(fma (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (sqrt (+ x 1)))
60.0ms	(/ x (sqrt (+ x 1)))
142.0ms	(fma (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
115.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify2.1s

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
3	3582
2	1026
1	374
0	190

prune547.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.3b

bsearch124.0ms

Steps

Iters	Range		Point
9	68.55102067575892	801012902.7811656	10076.446968341284
9	-17438.246738609338	-0.0018335887134067947	-1.0028494934768706

simplify13.0ms

Iterations

Iter	Nodes
done	54
2	54
1	45
0	27

end0.0ms

sample2.0s

Algorithm

intervals

Results

774.0ms	1695×	body	1280	valid
510.0ms	1221×	body	640	valid
364.0ms	4115×	body	80	valid
183.0ms	641×	body	320	valid
53.0ms	328×	body	160	valid