Details

sample65.0ms

Algorithm

intervals

Results

33.0ms	77×	body	1280	valid
13.0ms	54×	body	640	valid
6.0ms	21×	body	2560	valid
2.0ms	78×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	10	8
done	10	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b	(sqrt (+ (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series285.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ x (sqrt (+ (* x x) 1.0)))
186.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms	(sqrt (+ (* x x) 1.0))

simplify2.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (715.0ms)

Iter	Nodes	Cost
0	139	813
1	329	677
2	990	609
3	4695	547
done	5000	547

prune191.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series146.0ms

Counts

1 → 3

Calls

1 calls:

146.0ms

(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify353.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	168	256
3	959	256
done	5000	256

prune43.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (hypot (sqrt 1.0) x) x)
2.2b	(log (* 1 (+ (hypot (sqrt 1.0) x) x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log`
5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `rem-log-exp`
2×	`expm1-log1p-u` `log-div` `flip3-+` `associate-*r/` `prod-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `log-prod` `1-exp` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

2.0ms	(+ (hypot (sqrt 1.0) x) x)
4.0ms	(log (* 1 (+ (hypot (sqrt 1.0) x) x)))

series399.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(+ (hypot (sqrt 1.0) x) x)
274.0ms	(log (* 1 (+ (hypot (sqrt 1.0) x) x)))

simplify1.7s

Counts

40 → 40

Iterations

Useful iterations: 3 (516.0ms)

Iter	Nodes	Cost
0	103	499
1	258	452
2	852	404
3	4534	396
done	5000	396

prune100.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (hypot (sqrt 1.0) x) x)
0.5b	(+ (hypot (sqrt 1.0) x) x)
2.2b	(log (+ (hypot (sqrt 1.0) x) x))
2.2b	(log (+ (hypot (sqrt 1.0) x) x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
6×	`pow1` `add-exp-log` `fma-def`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 68

Calls

4 calls:

2.0ms	(+ (hypot (sqrt 1.0) x) x)
2.0ms	(+ (hypot (sqrt 1.0) x) x)
2.0ms	(log (+ (hypot (sqrt 1.0) x) x))
3.0ms	(log (+ (hypot (sqrt 1.0) x) x))

series810.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (hypot (sqrt 1.0) x) x)
129.0ms	(+ (hypot (sqrt 1.0) x) x)
276.0ms	(log (+ (hypot (sqrt 1.0) x) x))
280.0ms	(log (+ (hypot (sqrt 1.0) x) x))

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: 3 (329.0ms)

Iter	Nodes	Cost
0	102	1018
1	240	986
2	703	878
3	3367	862
done	5000	862

prune257.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch82.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.0009199034035155784
9	-5.7596417613087905	-6.7357437175194845e-09	-0.0007065730033359492

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	28	46
1	33	43
2	35	43
done	35	43

end0.0ms

sample1.9s

Algorithm

intervals

Results

945.0ms	2308×	body	1280	valid
368.0ms	1563×	body	640	valid
221.0ms	786×	body	2560	valid
107.0ms	767×	body	320	valid
70.0ms	2171×	body	80	valid
32.0ms	405×	body	160	valid