Details

sample53.0ms

Algorithm

intervals

Results

15.0ms	54×	body	640	valid
9.0ms	133×	body	80	valid
7.0ms	33×	body	320	valid
6.0ms	18×	body	1280	valid
2.0ms	18×	body	160	valid

simplify142.0ms

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: 11.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
3.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite801.0ms

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:

18.0ms	(/ 1.0 (- x 1.0))
128.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
12.0ms	(/ 1.0 (+ x 1.0))
585.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1.0 (- x 1.0))
75.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
38.0ms	(/ 1.0 (+ x 1.0))
263.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify3.0s

Counts

630 → 630

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	502	19834
1	1149	17345
2	2802	12902
done	5000	10138

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
2.4b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
12.9b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`fma-def`
8×	`add-log-exp`
6×	`pow1` `times-frac` `associate-*l/`
4×	`expm1-log1p-u` `flip3-+` `associate-l` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-sub` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `-commutative` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

31.0ms	(* (+ x 1.0) x)
9.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
135.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
55.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series598.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (+ x 1.0) x)
53.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
394.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
96.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify2.8s

Counts

104 → 104

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	166	1683
1	493	1597
2	1919	1205
done	5000	1196

prune356.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
0.1b	(/ 2.0 (pow x 5))
0.1b	(/ 2.0 (pow x 3))
0.1b	(/ 2.0 (pow x 7))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
85×	`*-un-lft-identity`
77×	`add-sqr-sqrt` `add-cube-cbrt`
45×	`unpow-prod-down`
26×	`associate-/r*`
25×	`fma-def`
19×	`add-exp-log`
15×	`sqr-pow`
12×	`cube-prod`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 205

Calls

4 calls:

107.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
15.0ms	(/ 2.0 (pow x 5))
10.0ms	(/ 2.0 (pow x 3))
8.0ms	(/ 2.0 (pow x 7))

series451.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
64.0ms	(/ 2.0 (pow x 5))
57.0ms	(/ 2.0 (pow x 3))
119.0ms	(/ 2.0 (pow x 7))

simplify976.0ms

Counts

217 → 217

Iterations

Useful iterations: done (970.0ms)

Iter	Nodes	Cost
0	263	2139
1	499	1870
2	1338	1802
done	5000	1801

prune877.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
0.1b	(/ 2.0 (pow x 5))
0.1b	(/ 2.0 (pow x 7))
0.1b	(/ (/ 2.0 x) (* x x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
74×	`*-un-lft-identity`
66×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`unpow-prod-down`
26×	`add-exp-log`
25×	`fma-def`
20×	`add-cbrt-cube`
19×	`associate-/l*`
15×	`associate-/r*`
12×	`div-exp`
11×	`sqr-pow`
8×	`cbrt-undiv` `div-inv`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

67.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
11.0ms	(/ 2.0 (pow x 5))
10.0ms	(/ 2.0 (pow x 7))
16.0ms	(/ (/ 2.0 x) (* x x))

series478.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
79.0ms	(/ 2.0 (pow x 5))
111.0ms	(/ 2.0 (pow x 7))
55.0ms	(/ (/ 2.0 x) (* x x))

simplify2.0s

Counts

198 → 198

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	271	1954
1	563	1761
2	1507	1641
done	5000	1640

prune766.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.9b

bsearch181.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	115.55938526424309
9	-1501.2167507114543	-0.006495210018506858	-117.27098644189155

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	65
1	41	65
done	41	65

end0.0ms

sample1.4s

Algorithm

intervals

Results

560.0ms	1895×	body	640	valid
258.0ms	903×	body	320	valid
221.0ms	4165×	body	80	valid
129.0ms	536×	body	1280	valid
48.0ms	503×	body	160	valid