Details

sample94.0ms

Algorithm

intervals

Results

45.0ms	134×	body	80	valid
23.0ms	59×	body	1280	valid
12.0ms	42×	body	640	valid
4.0ms	17×	body	320	valid
1.0ms	4×	body	160	valid

simplify219.0ms

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: 28.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
1.0b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite120.0ms

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:

8.0ms	(/ x (+ x 1))
18.0ms	(/ (+ x 1) (- x 1))
60.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1))
38.0ms	(/ (+ x 1) (- x 1))
122.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.6s

Counts

762 → 762

Iterations

Iter	Nodes
2	3080
1	1349
0	584

prune8.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (+ x 1) (- x 1))))
0.0b	(/ (+ x 1) (- x 1))
0.5b	(expm1 (/ (+ x 1) (- x 1)))
1.0b	(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
77×	`times-frac`
67×	`add-cube-cbrt`
54×	`prod-diff`
20×	`distribute-lft-out`
18×	`fma-neg`
12×	`difference-of-squares`
10×	`associate-/r/`
7×	`associate-/r*` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
5×	`flip3-+` `difference-of-sqr-1` `flip-+` `log1p-expm1-u` `div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `associate-/l*`
2×	`log1p-udef` `flip3--` `diff-log` `flip--` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `div-exp` `log1p-expm1` `expm1-udef`

Counts

4 → 173

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (+ x 1) (- x 1))))
36.0ms	(/ (+ x 1) (- x 1))
1.0ms	(expm1 (/ (+ x 1) (- x 1)))
35.0ms	(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(log1p (expm1 (/ (+ x 1) (- x 1))))
23.0ms	(/ (+ x 1) (- x 1))
74.0ms	(expm1 (/ (+ x 1) (- x 1)))
294.0ms	(- (/ x (+ x 1)) (log1p (expm1 (/ (+ x 1) (- x 1)))))

simplify4.5s

Counts

185 → 185

Iterations

Iter	Nodes
3	4102
2	1350
1	546
0	257

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x 3 (fma x x 1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

0.0ms

(fma x 3 (fma x x 1))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(fma x 3 (fma x x 1))

simplify860.0ms

Counts

14 → 14

Iterations

Iter	Nodes
4	2134
3	378
2	84
1	34
0	21

prune133.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.3b	(/ -3 (* x (* x x)))
0.3b	(/ -1 (* x x))
6.4b	(+ (/ -1 (* x x)) (+ (/ -3 x) (/ -3 (* x (* x x)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`times-frac` `add-log-exp`
7×	`fma-def` `prod-exp` `cbrt-unprod`
6×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `pow-prod-up`
4×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-l` `pow-prod-down` `div-inv` `distribute-lft-out`
2×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip-+`
1×	`pow2` `+-commutative` `associate-+r+` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

15.0ms	(* x (* x x))
13.0ms	(/ -3 (* x (* x x)))
6.0ms	(/ -1 (* x x))
101.0ms	(+ (/ -1 (* x x)) (+ (/ -3 x) (/ -3 (* x (* x x)))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* x (* x x))
55.0ms	(/ -3 (* x (* x x)))
27.0ms	(/ -1 (* x x))
29.0ms	(+ (/ -1 (* x x)) (+ (/ -3 x) (/ -3 (* x (* x x)))))

simplify7.3s

Counts

117 → 117

Iterations

Iter	Nodes
3	9673
2	1767
1	482
0	169

prune855.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.8b

bsearch150.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	13913.189376161075
10	-8.26555774309129e+15	-0.755072844465923	-18305.620511464476

simplify7.0ms

Iterations

Iter	Nodes
2	31
1	31
0	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

836.0ms	4172×	body	80	valid
696.0ms	1736×	body	1280	valid
473.0ms	1205×	body	640	valid
128.0ms	595×	body	320	valid
42.0ms	292×	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