Details

sample42.0ms

Algorithm

intervals

Results

16.0ms	64×	body	1280	valid
8.0ms	40×	body	640	valid
7.0ms	124×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid

simplify166.0ms

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: 31.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
2.3b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite129.0ms

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` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 750

Calls

3 calls:

21.0ms	(/ (+ x 1) (- x 1))
17.0ms	(/ x (+ x 1))
64.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (+ x 1) (- x 1))
26.0ms	(/ x (+ x 1))
130.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.8s

Counts

759 → 759

Iterations

Iter	Nodes
2	3097
1	1346
0	581

prune7.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.5b	(/ -3 (* (* x x) x))
0.8b	(/ 1 (* x x))
5.8b	(- (/ -3 (* (* x x) x)) (+ (/ 1 (* x x)) (/ 3 x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
42×	`prod-diff`
34×	`times-frac`
33×	`add-sqr-sqrt`
31×	`pow1`
30×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`div-inv`
23×	`add-cbrt-cube`
16×	`distribute-lft-out`
9×	`prod-exp` `add-log-exp`
7×	`pow-plus` `distribute-rgt-out` `fma-neg` `div-exp` `pow-prod-up` `cbrt-unprod`
6×	`pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`pow2` `associate-r` `pow-sqr` `frac-sub` `distribute-lft-out--`
2×	`rec-exp` `clear-num` `associate-/r*` `frac-2neg` `diff-log` `1-exp` `frac-add`
1×	`sum-log` `sub-neg` `flip3-+` `flip3--` `associate-l` `pow3` `*-commutative` `flip-+` `flip--` `associate--r+` `inv-pow` `sub-div` `difference-of-squares` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

18.0ms	(* (* x x) x)
19.0ms	(/ -3 (* (* x x) x))
12.0ms	(/ 1 (* x x))
110.0ms	(- (/ -3 (* (* x x) x)) (+ (/ 1 (* x x)) (/ 3 x)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* x x) x)
46.0ms	(/ -3 (* (* x x) x))
19.0ms	(/ 1 (* x x))
28.0ms	(- (/ -3 (* (* x x) x)) (+ (/ 1 (* x x)) (/ 3 x)))

simplify14.1s

Counts

174 → 174

Iterations

Iter	Nodes
3	7425
2	1989
1	588
0	217

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
9.6b	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
34.5b	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
54×	`associate-l`
52×	`*-un-lft-identity`
46×	`times-frac`
28×	`add-cube-cbrt`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`pow1` `associate-r` `prod-exp`
6×	`difference-of-sqr-1` `distribute-lft-out--` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 136

Calls

4 calls:

30.0ms	(* (/ 1 (- x 1)) (+ x 1))
35.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ 1 (- x 1)) (+ x 1))
28.0ms	(* (/ 1 (- x 1)) (+ x 1))
132.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
145.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify3.0s

Counts

148 → 148

Iterations

Iter	Nodes
3	3589
2	1244
1	513
0	154

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (- x 1)) (+ x 1))
0.1b	(* (/ 1 (- x 1)) (+ x 1))
9.6b	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
34.5b	(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
54×	`associate-l`
52×	`*-un-lft-identity`
46×	`times-frac`
28×	`add-cube-cbrt`
22×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`pow1` `associate-r` `prod-exp`
6×	`difference-of-sqr-1` `distribute-lft-out--` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 136

Calls

4 calls:

24.0ms	(* (/ 1 (- x 1)) (+ x 1))
24.0ms	(* (/ 1 (- x 1)) (+ x 1))
0.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ 1 (- x 1)) (+ x 1))
24.0ms	(* (/ 1 (- x 1)) (+ x 1))
100.0ms	(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
130.0ms	(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))

simplify3.7s

Counts

148 → 148

Iterations

Iter	Nodes
3	4060
2	1354
1	542
0	165

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.8b

bsearch133.0ms

Steps

Iters	Range		Point
8	0.9676876931049737	32461.898498684495	8293.699788933664
8	-426929.41805624013	-102.89153151738607	-9487.53105400853

simplify15.0ms

Iterations

Iter	Nodes
3	50
2	50
1	45
0	30

end0.0ms

sample2.5s

Algorithm

intervals

Results

848.0ms	1752×	body	1280	valid
764.0ms	4033×	body	80	valid
550.0ms	1260×	body	640	valid
156.0ms	648×	body	320	valid
49.0ms	307×	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