Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	93×	body	1280	valid
4.0ms	125×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `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

4 → 85

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series805.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 1.0 (hypot 1.0 x))
64.0ms	(hypot 1.0 x)
271.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
363.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify827.0ms

Counts

97 → 97

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	225	2149
1	536	1724
2	1590	1489
done	5000	1355

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
29.0ms	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.8s

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1.0 (hypot 1.0 x))
1.1s	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
469.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
113.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	342	3335
1	994	3143
2	3930	2907
done	5000	2906

prune370.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

357×	`times-frac`
276×	`*-un-lft-identity`
210×	`sqrt-prod`
172×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`distribute-lft-out`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
11×	`flip3-+` `flip-+`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`associate-/r*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*r/` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/2` `div-sub` `pow-prod-down`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

47.0ms	(/ (/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
262.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
264.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
120.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.8s

Counts

301 → 301

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	501	20339
1	1371	18084
2	4814	17156
done	5000	17155

prune674.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
0.9b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
18.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series789.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
275.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
128.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
112.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify861.0ms

Counts

79 → 79

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	164	1627
1	404	1493
2	1362	1360
done	5000	1313

prune349.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes189.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.7b

bsearch158.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.001967053414029855
9	-9.588134368690297e-05	-3.1186122123765165e-12	-8.847354589138371e-05

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	146
1	46	146
done	46	146

end0.0ms

sample851.0ms

Algorithm

intervals

Results

476.0ms	2991×	body	1280	valid
116.0ms	3958×	body	80	valid
75.0ms	609×	body	640	valid
29.0ms	308×	body	320	valid
7.0ms	134×	body	160	valid