Details

sample85.0ms

Algorithm

intervals

Results

29.0ms	57×	body	1280	valid
22.0ms	41×	body	640	valid
14.0ms	135×	body	80	valid
5.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify234.0ms

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: 28.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite163.0ms

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))
33.0ms	(/ (+ x 1) (- x 1))
85.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series159.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ x (+ x 1))
28.0ms	(/ (+ x 1) (- x 1))
101.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.2s

Counts

762 → 762

Iterations

Iter	Nodes
2	3080
1	1349
0	584

prune7.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

3664×	`*-un-lft-identity`
2832×	`times-frac`
2392×	`add-sqr-sqrt`
1836×	`prod-diff`
1492×	`add-cube-cbrt`
717×	`distribute-lft-out`
444×	`difference-of-squares`
318×	`associate-/r/`
255×	`distribute-lft-out--`
216×	`difference-of-sqr-1`
159×	`div-inv`
105×	`flip3-+` `flip3--` `flip-+` `flip--`
81×	`frac-times`
63×	`cbrt-div`
54×	`fma-neg`
51×	`frac-sub`
27×	`associate-*l/`
15×	`associate-*r/`
10×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 2053

Calls

4 calls:

390.0ms	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
76.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
80.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
71.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
107.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
113.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
116.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify3.3s

Counts

2065 → 2065

Iterations

Iter	Nodes
2	5388
1	1712
0	763

prune25.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (* (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
2.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
28.8b	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

2444×	`*-un-lft-identity`
1888×	`times-frac`
1596×	`add-sqr-sqrt`
1224×	`prod-diff`
996×	`add-cube-cbrt`
478×	`distribute-lft-out`
296×	`difference-of-squares`
212×	`associate-/r/`
170×	`distribute-lft-out--`
144×	`difference-of-sqr-1`
106×	`div-inv`
70×	`flip3-+` `flip-+`
46×	`flip3--` `flip--`
36×	`fma-neg`
15×	`cbrt-div` `associate-*r/`
10×	`frac-sub`
9×	`frac-times`
8×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`associate-*l/`
2×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `fma-udef`

Counts

4 → 1356

Calls

4 calls:

263.0ms	(cbrt (* (* (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
79.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
88.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
1.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

365.0ms	(cbrt (* (* (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
121.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
107.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
116.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify3.4s

Counts

1368 → 1368

Iterations

Iter	Nodes
2	3851
1	1474
0	642

prune22.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
16.2b	(/ x (- (* x x) (* 1 1)))
28.5b	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
30.6b	(fma (- (/ (cbrt (+ x 1)) (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1) (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

6.0ms	(cbrt (+ x 1))
22.0ms	(/ x (- (* x x) (* 1 1)))
1.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
1.0ms	(fma (- (/ (cbrt (+ x 1)) (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1) (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt (+ x 1))
75.0ms	(/ x (- (* x x) (* 1 1)))
150.0ms	(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
270.0ms	(fma (- (/ (cbrt (+ x 1)) (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1) (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1)))

simplify2.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	3648
2	1048
1	401
0	187

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch219.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	14245.787973373435
9	-128555.04713805256	-0.18430940072566707	-16169.55925066577

simplify21.0ms

Iterations

Iter	Nodes
4	45
3	45
2	43
1	38
0	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

745.0ms	1726×	body	1280	valid
626.0ms	575×	body	320	valid
444.0ms	1281×	body	640	valid
363.0ms	4132×	body	80	valid
77.0ms	286×	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