Details

sample75.0ms

Algorithm

intervals

Results

32.0ms	85×	body	1280	valid
21.0ms	139×	body	80	valid
6.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

18.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
10.0ms	(/ 1.0 (hypot 1.0 x))
29.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
13.0ms	(/ 1.0 (hypot 1.0 x))
100.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
134.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify4.2s

Counts

78 → 78

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	112	1034
1	223	951
2	539	887
3	1386	885
4	4985	881
done	5000	881

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 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)))))
1.2b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite75.0ms

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×	`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/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 90

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
27.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
25.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
16.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
264.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
96.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
42.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	163	2352
1	385	2241
2	1282	2071
done	5001	1894

prune330.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 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)))))
1.2b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
39×	`times-frac`
24×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*` `distribute-lft-out`
6×	`distribute-lft-out--` `add-log-exp`
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` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 106

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
47.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
18.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1.0 (hypot 1.0 x))
237.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
89.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
48.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify2.5s

Counts

118 → 118

Iterations

Useful iterations: 2 (242.0ms)

Iter	Nodes	Cost
0	180	2492
1	404	2387
2	1019	2261
3	2842	2261
done	5000	2261

prune417.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.6b

localize37.0ms

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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.2b	(pow (/ 0.5 (hypot 1.0 x)) 3)
1.2b	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`unpow-prod-down` `cube-prod`
26×	`times-frac`
24×	`difference-of-squares`
21×	`add-cube-cbrt`
11×	`sqr-pow`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`frac-times` `associate-r/` `associate-l*`
3×	`pow-unpow` `associate-r`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down` `associate-*l/` `pow-exp` `div-inv` `rem-cube-cbrt`
1×	`difference-cubes` `cbrt-undiv` `cube-div` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `pow1/2` `diff-log` `unpow3` `div-exp` `prod-exp` `sqrt-prod` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
47.0ms	(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
9.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
68.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series460.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
242.0ms	(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
57.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
80.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify2.2s

Counts

142 → 142

Iterations

Useful iterations: 2 (829.0ms)

Iter	Nodes	Cost
0	250	3432
1	773	3152
2	3293	2872
done	5000	2872

prune591.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.4b

regimes183.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.5b and baseline of 14.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	44
1	29	44
done	29	44

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2884×	body	1280	valid
611.0ms	4024×	body	80	valid
263.0ms	623×	body	640	valid
119.0ms	318×	body	320	valid
19.0ms	151×	body	160	valid