Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	54×	body	640	valid
5.0ms	133×	body	80	valid
4.0ms	33×	body	320	valid
3.0ms	18×	body	1280	valid
1.0ms	18×	body	160	valid

simplify162.0ms

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

localize20.0ms

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)))

rewrite638.0ms

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:

13.0ms	(/ 1.0 (- x 1.0))
107.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
22.0ms	(/ 1.0 (+ x 1.0))
435.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (- x 1.0))
64.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
30.0ms	(/ 1.0 (+ x 1.0))
263.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.8s

Counts

630 → 630

Iterations

Useful iterations: done (2.7s)

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

localize14.0ms

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))

rewrite164.0ms

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:

35.0ms	(* (+ x 1.0) x)
9.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
82.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
34.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series588.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (+ x 1.0) x)
56.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
392.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
88.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: done (2.6s)

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

prune349.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite137.0ms

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:

92.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
13.0ms	(/ 2.0 (pow x 5))
9.0ms	(/ 2.0 (pow x 3))
8.0ms	(/ 2.0 (pow x 7))

series471.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
80.0ms	(/ 2.0 (pow x 5))
57.0ms	(/ 2.0 (pow x 3))
88.0ms	(/ 2.0 (pow x 7))

simplify1.2s

Counts

217 → 217

Iterations

Useful iterations: done (1.2s)

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

prune913.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize32.0ms

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))

rewrite158.0ms

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:

90.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
15.0ms	(/ 2.0 (pow x 5))
15.0ms	(/ 2.0 (pow x 7))
30.0ms	(/ (/ 2.0 x) (* x x))

series463.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 5)))
67.0ms	(/ 2.0 (pow x 5))
101.0ms	(/ 2.0 (pow x 7))
41.0ms	(/ (/ 2.0 x) (* x x))

simplify1.6s

Counts

198 → 198

Iterations

Useful iterations: done (1.5s)

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

prune908.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 25.9b

bsearch154.0ms

Steps

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

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	67
1	40	67
done	40	67

end0.0ms

sample2.0s

Algorithm

intervals

Results

672.0ms	536×	body	1280	valid
628.0ms	1895×	body	640	valid
249.0ms	4165×	body	80	valid
155.0ms	903×	body	320	valid
60.0ms	503×	body	160	valid