Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	55×	body	640	valid
4.0ms	135×	body	80	valid
3.0ms	22×	body	1280	valid
2.0ms	31×	body	320	valid
1.0ms	13×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	52	15
5	59	15
6	71	15
7	92	15
8	110	15
9	117	15
done	117	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
50.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
220.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
29.0ms	(/ 1.0 (+ x 1.0))
43.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
220.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.1s

Counts

630 → 630

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	502	19834
1	1100	17345
2	3063	12902
done	5000	12830

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
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))
30.0b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite44.0ms

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:

3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
16.0ms	(/ (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)))
21.0ms	(* (* (+ x 1.0) x) (- x 1.0))
0.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series615.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
305.0ms	(/ (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)))
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
179.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify996.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (398.0ms)

Iter	Nodes	Cost
0	227	3140
1	630	2926
2	2575	2460
done	5000	2460

prune272.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (pow x 5))
0.2b	(/ 2.0 (pow x 7))
0.9b	(/ 2.0 (pow x 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
26×	`associate-/r*`
18×	`add-exp-log`
12×	`cube-prod` `sqr-pow`
9×	`div-exp` `add-cbrt-cube` `associate-/l*`
4×	`cube-mult` `unpow3`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

3 → 161

Calls

3 calls:

3.0ms	(/ 2.0 (pow x 5))
4.0ms	(/ 2.0 (pow x 7))
4.0ms	(/ 2.0 (pow x 3))

series150.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ 2.0 (pow x 5))
57.0ms	(/ 2.0 (pow x 7))
40.0ms	(/ 2.0 (pow x 3))

simplify553.0ms

Counts

170 → 170

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	234	1776
1	427	1542
2	1377	1494
done	5000	1494

prune389.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (pow x 5))
0.1b	(* (/ 1 (* x x)) (/ 2.0 x))
0.2b	(/ 2.0 (pow x 7))
0.5b	(/ 1 (* x x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
64×	`times-frac`
60×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
25×	`div-exp`
24×	`unpow-prod-down`
23×	`prod-exp`
15×	`associate-/r*`
14×	`pow1`
13×	`associate-r`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`sqr-pow`
7×	`associate-l`
6×	`rec-exp` `pow-flip` `1-exp` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-prod-down` `pow-exp`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `inv-pow`

Counts

4 → 188

Calls

4 calls:

3.0ms	(/ 2.0 (pow x 5))
20.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
3.0ms	(/ 2.0 (pow x 7))
5.0ms	(/ 1 (* x x))

series162.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 2.0 (pow x 5))
40.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
57.0ms	(/ 2.0 (pow x 7))
20.0ms	(/ 1 (* x x))

simplify987.0ms

Counts

200 → 200

Iterations

Useful iterations: 2 (405.0ms)

Iter	Nodes	Cost
0	277	2109
1	641	1798
2	2511	1551
done	5000	1551

prune438.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes60.0ms

Accuracy

94.8% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 9.7b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	102
1	48	102
done	48	102

end0.0ms

sample599.0ms

Algorithm

intervals

Results

206.0ms	1886×	body	640	valid
123.0ms	4185×	body	80	valid
78.0ms	961×	body	320	valid
74.0ms	550×	body	1280	valid
23.0ms	420×	body	160	valid