Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	81×	body	1280	valid
7.0ms	142×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	30	12
4	32	12
5	38	12
6	41	12
done	41	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 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))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series741.0ms

Counts

3 → 9

Calls

3 calls:

279.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
106.0ms	(/ 1.0 (hypot 1.0 x))
355.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify724.0ms

Counts

84 → 84

Iterations

Useful iterations: done (720.0ms)

Iter	Nodes	Cost
0	207	2042
1	487	1618
2	1465	1398
done	5001	1381

prune219.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.4b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series661.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
104.0ms	(/ 1.0 (hypot 1.0 x))
109.0ms	(/ 1.0 (hypot 1.0 x))
114.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify762.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (323.0ms)

Iter	Nodes	Cost
0	190	1534
1	490	1450
2	1599	1315
done	5001	1315

prune347.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(/ 1.0 (sqrt (hypot 1.0 x)))
0.2b	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
1.5b	(- (* 1.0 1.0) (* (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) 0.5))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 251

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
15.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) 0.5))

series698.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
143.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
112.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
119.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) 0.5))

simplify1.2s

Counts

263 → 263

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	411	5989
1	1011	5095
2	2729	4691
done	5000	4687

prune624.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
24×	`prod-diff`
17×	`log-prod`
14×	`exp-sum`
9×	`times-frac`
8×	`pow1`
7×	`sqrt-prod`
6×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sub-neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

278.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
104.0ms	(/ 1.0 (hypot 1.0 x))
371.0ms	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
368.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify730.0ms

Counts

121 → 121

Iterations

Useful iterations: done (725.0ms)

Iter	Nodes	Cost
0	268	3461
1	557	2603
2	1555	2176
done	5000	2151

prune341.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes252.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	77
1	43	77
done	43	77

end0.0ms

sample808.0ms

Algorithm

intervals

Results

473.0ms	2868×	body	1280	valid
114.0ms	4056×	body	80	valid
73.0ms	576×	body	640	valid
31.0ms	358×	body	320	valid
8.0ms	142×	body	160	valid