Details

sample70.0ms

Algorithm

intervals

Results

25.0ms	93×	body	1280	valid
23.0ms	131×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	43	12
done	43	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `sqrt-prod` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

1.0ms	(hypot 1.0 x)
33.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
10.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(hypot 1.0 x)
140.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
136.0ms	(/ 1.0 (hypot 1.0 x))
512.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.8s

Counts

99 → 99

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	225	2015
1	566	1622
2	2425	1367
done	5001	1350

prune427.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
10.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series909.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ 1.0 (hypot 1.0 x))
120.0ms	(/ 1.0 (hypot 1.0 x))
456.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
177.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.9s

Counts

103 → 103

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	190	1534
1	515	1452
2	2583	1320
done	5001	1315

prune421.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b	(pow (/ 1.0 (hypot 1.0 x)) 3)
1.5b	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
20.6b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `fma-def`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `flip3-+` `fma-neg` `pow1/3` `diff-log` `div-exp` `prod-diff` `sum-log` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
11.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series977.0ms

Counts

4 → 12

Calls

4 calls:

445.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
275.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
126.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
130.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify2.7s

Counts

137 → 137

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	276	2443
1	906	2015
2	4756	1796
done	5000	1796

prune565.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0b	(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5b	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
20.6b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`unpow-prod-down` `cube-prod`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`div-inv`
1×	`cube-div` `cube-mult` `sub-neg` `cbrt-div` `log1p-udef` `expm1-log1p` `flip3--` `fma-neg` `pow1/3` `diff-log` `unpow3` `log1p-expm1` `prod-diff` `flip--` `rem-cbrt-cube` `expm1-udef` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

0.0ms	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0ms	(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series2.9s

Counts

4 → 12

Calls

4 calls:

1.6s	(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.1s	(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
153.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
131.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify552.0ms

Counts

94 → 94

Iterations

Useful iterations: done (548.0ms)

Iter	Nodes	Cost
0	289	2249
1	918	1834
done	5000	1672

prune365.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes230.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 15.3b

bsearch218.0ms

Steps

Iters	Range		Point
9	0.00015484893005477947	28918.939680702064	0.9579305759277074
10	-2676750800.736259	-2.9526231381329305e-09	-0.0024393164175487893

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	102
1	54	102
done	54	102

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2878×	body	1280	valid
550.0ms	4062×	body	80	valid
137.0ms	315×	body	320	valid
135.0ms	593×	body	640	valid
16.0ms	152×	body	160	valid