Details

sample55.0ms

Algorithm

intervals

Results

24.0ms	87×	body	1280	valid
7.0ms	139×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	24
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms	(hypot 1.0 x)
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series171.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(hypot 1.0 x)
12.0ms	(/ 1.0 (hypot 1.0 x))
113.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2619
2	650
1	220
0	101

prune274.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
0.0b	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)))
1.1b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
11×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`sum-log`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `associate-/r/` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`+-commutative` `associate-+l+` `sub-neg` `diff-log` `div-sub`

Counts

4 → 84

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
376.0ms	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
657.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)))
132.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

series990.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
200.0ms	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
571.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)))
205.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

simplify2.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
2	1596
1	428
0	161

prune689.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
0.5b	(/ (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)) (sqrt (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))))
1.1b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))
1.1b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`add-log-exp`
12×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`sum-log` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `flip3-+` `sqrt-div` `diff-log` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 80

Calls

4 calls:

345.0ms	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
1.0s	(/ (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)) (sqrt (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))))
104.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))
111.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

series1.1s

Counts

4 → 12

Calls

4 calls:

189.0ms	(+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0))
561.0ms	(/ (+ (+ (* 1.0 (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* 1.0 1.0)) (sqrt (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))))
187.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))
211.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

simplify2.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1166
1	349
0	142

prune653.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1.0 (hypot 1.0 x)))
0.3b	(cbrt (/ 1.0 (hypot 1.0 x)))
0.3b	(cbrt (/ 1.0 (hypot 1.0 x)))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (* (* (cbrt (/ 1.0 (hypot 1.0 x))) (cbrt (/ 1.0 (hypot 1.0 x)))) (cbrt (/ 1.0 (hypot 1.0 x))))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac`
25×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

4.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
4.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
4.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
9.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (* (* (cbrt (/ 1.0 (hypot 1.0 x))) (cbrt (/ 1.0 (hypot 1.0 x)))) (cbrt (/ 1.0 (hypot 1.0 x))))))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
260.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
187.0ms	(cbrt (/ 1.0 (hypot 1.0 x)))
179.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (* (* (cbrt (/ 1.0 (hypot 1.0 x))) (cbrt (/ 1.0 (hypot 1.0 x)))) (cbrt (/ 1.0 (hypot 1.0 x))))))))

simplify3.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
4	4387
3	1145
2	374
1	160
0	96

prune529.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.0b

regimes397.0ms

Accuracy

0% (0.0b remaining)

Error of 15.1b against oracle of 15.1b and baseline of 15.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	2834×	body	1280	valid
317.0ms	4078×	body	80	valid
156.0ms	592×	body	640	valid
72.0ms	177×	body	160	valid
63.0ms	319×	body	320	valid