Details

sample79.0ms

Algorithm

intervals

Results

23.0ms	58×	body	640	valid
15.0ms	137×	body	80	valid
13.0ms	17×	body	160	valid
8.0ms	28×	body	320	valid
8.0ms	16×	body	1280	valid

simplify174.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.7b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
17.0ms	(/ 1 (+ x 1))
50.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
172.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1 (- x 1))
14.0ms	(/ 1 (+ x 1))
27.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
122.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify4.5s

Counts

660 → 660

Iterations

Iter	Nodes
2	2750
1	1122
0	495

prune4.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1))
0.3b	(cbrt (- x 1))
0.3b	(* (cbrt (- x 1)) (cbrt (- x 1)))
16.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (* (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (/ 1 (cbrt (- x 1)))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

363×	`*-un-lft-identity`
329×	`times-frac`
298×	`add-sqr-sqrt`
245×	`add-cube-cbrt`
236×	`associate-+l+`
234×	`prod-diff`
54×	`cbrt-prod`
40×	`distribute-lft-out`
32×	`div-inv`
26×	`associate-/r/`
20×	`difference-of-squares`
16×	`cbrt-div`
14×	`flip3-+` `swap-sqr` `flip-+`
13×	`fma-def`
12×	`flip3--` `frac-add` `flip--` `distribute-lft-out--`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`add-log-exp`
8×	`pow1/3` `difference-of-sqr-1`
7×	`frac-times`
6×	`add-exp-log`
5×	`associate-l/` `associate-r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `frac-sub` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`un-div-inv`
2×	`sum-log` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `+-commutative` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod`

Counts

4 → 384

Calls

4 calls:

6.0ms	(cbrt (- x 1))
5.0ms	(cbrt (- x 1))
51.0ms	(* (cbrt (- x 1)) (cbrt (- x 1)))
241.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (* (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (/ 1 (cbrt (- x 1)))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (- x 1))
64.0ms	(cbrt (- x 1))
89.0ms	(* (cbrt (- x 1)) (cbrt (- x 1)))
176.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (* (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (/ 1 (cbrt (- x 1)))))

simplify1.8s

Counts

396 → 396

Iterations

Iter	Nodes
2	2849
1	885
0	341

prune4.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(* (+ x 1) x)
0.1b	(* (* (+ x 1) x) (- x 1))
29.3b	(fma (- x (* 2 (+ x 1))) (+ x -1) (* (+ x 1) x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
13×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
12×	`associate-*l/`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-l`
5×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `associate-*r/` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`difference-of-sqr-1` `fma-udef` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

17.0ms	(* (+ x 1) x)
20.0ms	(* (+ x 1) x)
45.0ms	(* (* (+ x 1) x) (- x 1))
0.0ms	(fma (- x (* 2 (+ x 1))) (+ x -1) (* (+ x 1) x))

series507.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (+ x 1) x)
70.0ms	(* (+ x 1) x)
160.0ms	(* (* (+ x 1) x) (- x 1))
195.0ms	(fma (- x (* 2 (+ x 1))) (+ x -1) (* (+ x 1) x))

simplify4.5s

Counts

126 → 126

Iterations

Iter	Nodes
3	4826
2	1218
1	466
0	160

prune942.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1) x)
0.1b	(* (* (+ x 1) x) (- x 1))
0.3b	(/ 2 (* (* (+ x 1) x) (- x 1)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff` `associate-*l/`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `associate-r`
8×	`frac-times` `associate-/r/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`pow-prod-down` `associate-*r/`
3×	`expm1-log1p-u` `cbrt-undiv` `times-frac` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `*-commutative` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `difference-of-sqr-1` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 113

Calls

3 calls:

29.0ms	(* (+ x 1) x)
44.0ms	(* (* (+ x 1) x) (- x 1))
47.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (+ x 1) x)
132.0ms	(* (* (+ x 1) x) (- x 1))
97.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify8.1s

Counts

122 → 122

Iterations

Iter	Nodes
3	6765
2	1644
1	603
0	207

prune685.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	1854×	body	640	valid
509.0ms	4184×	body	80	valid
397.0ms	538×	body	1280	valid
337.0ms	946×	body	320	valid
132.0ms	483×	body	160	valid