Details

sample34.0ms

Algorithm

intervals

Results

15.0ms	93×	body	1280	valid
6.0ms	129×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6
done	37	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize8.0ms

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)))))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `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` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
75.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
86.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1998	411
3	5001	411
done	5001	411

prune147.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.6b

localize13.0ms

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 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-*r/`
6×	`add-log-exp`
4×	`pow1` `flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 110

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
41.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
159.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify53.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	407	1275
1	1594	1181
2	5001	1177
done	5001	1177

prune303.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
1.7b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
41×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
25×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`associate-*l/`
14×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
11×	`flip3-+` `flip-+` `associate-/l*`
8×	`prod-exp` `associate-/r*` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out`
7×	`associate-/l/`
6×	`flip3--` `flip--` `add-log-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log`

Counts

4 → 136

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
36.0ms	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
59.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
24.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
212.0ms	(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
59.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
34.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify117.0ms

Counts

148 → 148

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	832	2943
1	4603	2523
2	5001	2523
done	5001	2523

prune445.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
0.1b	(exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))))
1.7b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
47×	`times-frac`
42×	`log-prod` `exp-sum`
27×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-*l/`
18×	`add-cbrt-cube`
17×	`add-exp-log`
16×	`associate-/r/`
14×	`associate-*r/`
12×	`flip3-+` `flip-+`
11×	`distribute-lft-out` `associate-/l*`
8×	`frac-sub` `div-inv`
7×	`associate-/l/`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`exp-prod` `prod-exp` `cbrt-unprod`
2×	`log-div` `frac-2neg` `exp-diff` `clear-num` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 136

Calls

4 calls:

94.0ms	(/ (exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
58.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
54.0ms	(exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))))
23.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
59.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
65.0ms	(exp (log (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))))
33.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify106.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	745	3547
1	3819	3193
2	5001	3107
done	5001	3107

prune489.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

regimes51.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15
done	21	15

end0.0ms

sample824.0ms

Algorithm

intervals

Results

458.0ms	2900×	body	1280	valid
108.0ms	3970×	body	80	valid
78.0ms	626×	body	640	valid
28.0ms	334×	body	320	valid
9.0ms	170×	body	160	valid