Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	54×	body	640	valid
8.0ms	140×	body	80	valid
5.0ms	34×	body	320	valid
4.0ms	13×	body	1280	valid
2.0ms	15×	body	160	valid

simplify203.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	50	15
5	55	15
6	64	15
7	82	15
8	99	15
9	109	15
done	109	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite719.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 583

Calls

3 calls:

13.0ms	(/ 1.0 (- x 1.0))
134.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
495.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series510.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ 1.0 (- x 1.0))
82.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
393.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify3.3s

Counts

592 → 592

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	485	19448
1	1101	16993
2	2675	12566
done	5002	9801

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
29.2b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

40.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
69.0ms	(* (* (+ x 1.0) x) (- x 1.0))
16.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series966.0ms

Counts

4 → 12

Calls

4 calls:

472.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
133.0ms	(* (* (+ x 1.0) x) (- x 1.0))
59.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
301.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify2.4s

Counts

123 → 123

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	227	3140
1	617	2926
2	2314	2478
done	5002	2453

prune450.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.3b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

31.0ms	(* (+ x 1.0) x)
94.0ms	(* (* (+ x 1.0) x) (- x 1.0))
54.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series307.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(* (+ x 1.0) x)
120.0ms	(* (* (+ x 1.0) x) (- x 1.0))
102.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	206	1975
1	542	1770
2	1995	1511
done	5000	1486

prune295.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
0.1b	(/ 2.0 (* (+ x 1.0) x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
51×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/` `associate-/r/`
12×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-l`
3×	`expm1-log1p-u` `associate-r` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 128

Calls

3 calls:

26.0ms	(* (+ x 1.0) x)
33.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
13.0ms	(/ 2.0 (* (+ x 1.0) x))

series223.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (+ x 1.0) x)
108.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
49.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify1.5s

Counts

137 → 137

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	227	2149
1	570	2040
2	1790	1872
done	5001	1864

prune399.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
done	14	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

687.0ms	4203×	body	80	valid
433.0ms	1862×	body	640	valid
233.0ms	554×	body	1280	valid
180.0ms	927×	body	320	valid
44.0ms	455×	body	160	valid