Details

sample63.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	nan
9.0ms	44×	body	1280	valid
9.0ms	54×	body	640	valid
5.0ms	124×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite796.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

15.0ms	(sqrt (+ x 1.0))
778.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series181.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(sqrt (+ x 1.0))
126.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify8.5s

Counts

41 → 41

Iterations

Iter	Nodes
done	5112
4	4828
3	1481
2	513
1	188
0	84

prune300.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
43×	`distribute-lft-out`
32×	`sqrt-prod`
30×	`times-frac`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
7×	`distribute-lft-out--`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 88

Calls

3 calls:

16.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
209.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

series492.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(sqrt (+ x 1.0))
122.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
316.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify10.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	4422
2	1289
1	410
0	166

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (- x x)) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
15×	`times-frac`
13×	`cbrt-prod`
11×	`distribute-lft-out`
10×	`associate-r`
9×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`distribute-lft-out--` `add-log-exp`
3×	`associate-l` `associate-/r*` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate-+r-` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 97

Calls

4 calls:

282.0ms	(/ (+ 1.0 (- x x)) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
48.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
8.0ms	(cbrt (+ x 1.0))
8.0ms	(cbrt (+ x 1.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

669.0ms	(/ (+ 1.0 (- x x)) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
288.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
392.0ms	(cbrt (+ x 1.0))
886.0ms	(cbrt (+ x 1.0))

simplify8.3s

Counts

109 → 109

Iterations

Iter	Nodes
done	5003
2	3868
1	933
0	342

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1602×	`*-un-lft-identity`
1100×	`sqrt-prod`
954×	`times-frac`
640×	`distribute-lft-out`
334×	`add-sqr-sqrt`
332×	`add-cube-cbrt`
100×	`distribute-lft-out--`
56×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`associate-+r-` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 649

Calls

4 calls:

84.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
85.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
187.0ms	(/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
391.0ms	(/ (/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series2.0s

Counts

4 → 12

Calls

4 calls:

321.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
299.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
960.0ms	(/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
435.0ms	(/ (/ (+ 1.0 (- x x)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify9.8s

Counts

661 → 661

Iterations

Iter	Nodes
done	5064
2	2845
1	1114
0	456

prune5.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes515.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.1s	7895×	body	80	nan
1.5s	4136×	body	80	valid
858.0ms	1236×	body	640	valid
763.0ms	1683×	body	1280	valid
120.0ms	620×	body	320	valid
72.0ms	325×	body	160	valid