Details

sample56.0ms

Algorithm

intervals

Results

22.0ms	128×	body	80	valid
11.0ms	65×	body	640	valid
5.0ms	22×	body	1280	valid
3.0ms	22×	body	320	valid
2.0ms	19×	body	160	valid

simplify165.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	198
9	198
8	170
7	103
6	83
5	72
4	60
3	41
2	31
1	18
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize22.0ms

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))
1.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite947.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `flip3--` `frac-add` `log1p-expm1-u` `flip--` `associate-/l*`
2×	`sum-log` `sub-neg` `diff-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `associate-+l-`

Counts

3 → 583

Calls

3 calls:

15.0ms	(/ 1.0 (- x 1.0))
87.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
777.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series375.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ 1.0 (- x 1.0))
55.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
290.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.4s

Counts

592 → 592

Iterations

Iter	Nodes
done	5000
2	2900
1	1136
0	484

prune2.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* 2.0 (+ x 1.0)))
0.0b	(/ (fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0))) (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
31.5b	(fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`prod-diff` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-*l/`
12×	`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*`
2×	`associate--r+`
1×	`clear-num` `associate-/r` `frac-2neg` `fma-neg` `diff-log` `associate-l` `-commutative` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

13.0ms	(- (* 1.0 x) (* 2.0 (+ x 1.0)))
59.0ms	(/ (fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0))) (* (* (+ x 1.0) x) (- x 1.0)))
72.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0)))

series964.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* 1.0 x) (* 2.0 (+ x 1.0)))
441.0ms	(/ (fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0))) (* (* (+ x 1.0) x) (- x 1.0)))
174.0ms	(* (* (+ x 1.0) x) (- x 1.0))
296.0ms	(fma (- x 1.0) (- (* 1.0 x) (* 2.0 (+ x 1.0))) (* (* 1.0 x) (+ x 1.0)))

simplify2.9s

Counts

125 → 125

Iterations

Iter	Nodes
done	5002
2	2778
1	682
0	230

prune585.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.6b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-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`
8×	`frac-times` `associate-r` `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` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 108

Calls

3 calls:

15.0ms	(* (+ x 1.0) x)
66.0ms	(* (* (+ x 1.0) x) (- x 1.0))
56.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series398.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* (+ x 1.0) x)
159.0ms	(* (* (+ x 1.0) x) (- x 1.0))
159.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1912
1	612
0	206

prune390.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
0.3b	(/ 2.0 (* (+ x 1.0) x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
51×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out` `unswap-sqr` `associate-/l/`

Counts

3 → 128

Calls

3 calls:

30.0ms	(* (+ x 1.0) x)
41.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
23.0ms	(/ 2.0 (* (+ x 1.0) x))

series250.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (+ x 1.0) x)
146.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
51.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify1.9s

Counts

137 → 137

Iterations

Iter	Nodes
done	5003
2	1981
1	607
0	227

prune576.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	1824×	body	640	valid
293.0ms	4228×	body	80	valid
245.0ms	905×	body	320	valid
164.0ms	592×	body	1280	valid
58.0ms	455×	body	160	valid