Details

sample71.0ms

Algorithm

intervals

Results

22.0ms	52×	body	1280	valid
13.0ms	39×	body	640	valid
11.0ms	136×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid

simplify157.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite161.0ms

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))
27.0ms	(/ (+ x 1) (- x 1))
80.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1))
32.0ms	(/ (+ x 1) (- x 1))
97.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.7s

Counts

762 → 762

Iterations

Iter	Nodes
2	3080
1	1349
0	584

prune3.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))
2.8b	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

rewrite195.0ms

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))
69.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
52.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
47.0ms	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ x 1) (- x 1))
52.0ms	(cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1))))
40.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
131.0ms	(- (/ x (+ x 1)) (cbrt (* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))))

simplify1.7s

Counts

376 → 376

Iterations

Iter	Nodes
2	3367
1	1187
0	403

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (+ x 1) (- x 1)))
0.0b	(cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1))))
0.0b	(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
2.8b	(- (/ x (+ x 1)) (cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1)))))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

442×	`*-un-lft-identity`
287×	`add-sqr-sqrt`
283×	`times-frac`
277×	`cbrt-prod`
163×	`cbrt-div`
138×	`add-cube-cbrt`
99×	`frac-times`
80×	`distribute-lft-out`
75×	`swap-sqr` `associate-*l/`
72×	`prod-diff`
62×	`difference-of-squares`
47×	`associate-*r/`
37×	`associate-r` `associate-l` `distribute-lft-out--`
36×	`difference-of-sqr-1`
31×	`frac-sub`
20×	`associate-/r/`
18×	`fma-neg`
11×	`pow1`
10×	`div-inv`
9×	`unswap-sqr`
8×	`pow1/3`
6×	`flip3--` `add-exp-log` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 410

Calls

4 calls:

9.0ms	(cbrt (/ (+ x 1) (- x 1)))
454.0ms	(cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1))))
61.0ms	(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
88.0ms	(- (/ x (+ x 1)) (cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1)))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (/ (+ x 1) (- x 1)))
57.0ms	(cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1))))
101.0ms	(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
106.0ms	(- (/ x (+ x 1)) (cbrt (* (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))) (/ (+ x 1) (- x 1)))))

simplify2.3s

Counts

422 → 422

Iterations

Iter	Nodes
2	5195
1	1501
0	618

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
14.6b	(/ x (- (* x x) (* 1 1)))
28.2b	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (/ (+ x 1) (- x 1))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
40×	`times-frac`
25×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`associate-/r*`
8×	`distribute-lft-out`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`associate-/r/`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--` `associate-/l/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

3 → 105

Calls

3 calls:

29.0ms	(/ (+ x 1) (- x 1))
22.0ms	(/ x (- (* x x) (* 1 1)))
1.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (/ (+ x 1) (- x 1))))

series272.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ (+ x 1) (- x 1))
80.0ms	(/ x (- (* x x) (* 1 1)))
168.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (/ (+ x 1) (- x 1))))

simplify4.9s

Counts

114 → 114

Iterations

Iter	Nodes
3	3785
2	1047
1	403
0	190

prune856.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch185.0ms

Steps

Iters	Range		Point
10	0.002603609100038161	6235082944194588.0	10675.910301293761
9	-710549284.1101115	-145.89507053458865	-12183.867794727486

simplify7.0ms

Iterations

Iter	Nodes
2	29
1	29
0	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	1774×	body	1280	valid
457.0ms	1198×	body	640	valid
406.0ms	4114×	body	80	valid
150.0ms	600×	body	320	valid
52.0ms	314×	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