Details

sample90.0ms

Algorithm

intervals

Results

51.0ms	101×	body	1280	valid
9.0ms	26×	body	640	valid
9.0ms	108×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	90
5	90
4	71
3	55
2	39
1	21
0	9

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
2.8b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16` `difference-of-squares`
3×	`associate-/r` `distribute-lft-out` `associate-/l` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `div-inv` `flip--`

Counts

4 → 78

Calls

4 calls:

18.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
25.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
9.0ms	(/ 1/2 (hypot 1 x))
85.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
33.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(/ 1/2 (hypot 1 x))
52.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	2029
2	747
1	247
0	118

prune319.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
2.3b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite917.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
36×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-lft-out`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate--r+` `associate-/l/`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 116

Calls

4 calls:

9.0ms	(/ 1/2 (hypot 1 x))
9.0ms	(/ 1/2 (hypot 1 x))
888.0ms	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
5.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1/2 (hypot 1 x))
9.0ms	(/ 1/2 (hypot 1 x))
214.0ms	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
125.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5004
2	1411
1	361
0	143

prune686.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.6b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ (log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
2.3b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
2.3b	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite928.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
51×	`times-frac`
48×	`distribute-lft-out`
36×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`log-pow`
24×	`exp-prod`
12×	`pow1`
10×	`associate-/l*`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`log-prod`
4×	`insert-posit16`
2×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `exp-diff` `div-exp` `exp-sum` `associate-/r/` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `div-sub` `rem-log-exp` `flip-+` `flip--`

Counts

4 → 133

Calls

4 calls:

9.0ms	(/ 1/2 (hypot 1 x))
880.0ms	(/ (log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
9.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
22.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1/2 (hypot 1 x))
203.0ms	(/ (log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
115.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
117.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

simplify1.7s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1294
1	393
0	186

prune708.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

localize141.0ms

Local error

Found 4 expressions with local error:

2.3b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
2.3b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
2.3b	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))
2.3b	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt` `add-log-exp`
6×	`pow1` `exp-prod`
4×	`sub-neg` `add-cbrt-cube` `exp-sum` `add-exp-log` `insert-posit16` `associate--r+`
2×	`distribute-rgt-in` `log-div` `distribute-lft-in` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 68

Calls

4 calls:

5.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
5.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
12.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))
18.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
111.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
144.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))
124.0ms	(log (exp (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

simplify5.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
4	4972
3	1237
2	385
1	148
0	66

prune665.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

regimes96.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	2850×	body	1280	valid
285.0ms	4068×	body	80	valid
276.0ms	638×	body	640	valid
57.0ms	304×	body	320	valid
18.0ms	140×	body	160	valid