Details

sample63.0ms

Algorithm

intervals

Results

33.0ms	86×	body	1280	valid
9.0ms	142×	body	80	valid
5.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify36.0ms

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: 13.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`add-exp-log` `add-cube-cbrt` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

18.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
24.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series249.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
117.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.0s

Counts

33 → 33

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	64	571
1	139	516
2	350	480
3	964	478
4	3190	476
done	5000	470

prune139.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize19.0ms

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 (- 1.0 (+ (/ 0.5 (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)))))
1.4b	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
79.0ms	(/ (* 1.0 (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
17.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
52.0ms	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

series566.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
266.0ms	(/ (* 1.0 (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
118.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
55.0ms	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

simplify1.4s

Counts

81 → 81

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	132	1780
1	351	1681
2	1159	1467
done	5000	1461

prune373.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
0.0b	(/ (* (- 0.5 (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.3b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`pow1`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
4×	`times-frac` `sqrt-div` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `associate-l/` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-unprod` `diff-log` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

17.0ms	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
30.0ms	(/ (* (- 0.5 (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
87.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))
306.0ms	(/ (* (- 0.5 (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
98.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
40.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: 2 (303.0ms)

Iter	Nodes	Cost
0	155	1913
1	387	1794
2	1293	1600
done	5000	1600

prune366.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
0.5b	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.3b	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

299×	`add-sqr-sqrt`
157×	`times-frac`
120×	`difference-of-squares`
113×	`*-un-lft-identity`
103×	`unpow-prod-down` `cube-prod`
61×	`add-cube-cbrt`
51×	`sqr-pow`
33×	`associate-/l*`
25×	`distribute-lft-out--`
11×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
9×	`pow1`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`difference-cubes`
4×	`unswap-sqr`
3×	`pow-unpow` `pow-prod-down` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*r/` `div-exp` `pow-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `sqrt-unprod` `diff-log` `unpow3` `div-sub` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 273

Calls

4 calls:

180.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
13.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
57.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
67.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series534.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
67.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
137.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
96.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify2.4s

Counts

285 → 285

Iterations

Useful iterations: 2 (877.0ms)

Iter	Nodes	Cost
0	353	10402
1	876	9946
2	2992	9672
done	5000	9672

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.2b

regimes49.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	69
1	35	69
done	35	69

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	2806×	body	1280	valid
318.0ms	4099×	body	80	valid
290.0ms	641×	body	640	valid
50.0ms	286×	body	320	valid
19.0ms	168×	body	160	valid