Details

sample59.0ms

Algorithm

intervals

Results

11.0ms	59×	body	640	valid
11.0ms	44×	body	1280	valid
10.0ms	260×	body	80	nan
6.0ms	126×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `hypot-def` `flip--`

Counts

4 → 758

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
9.0ms	(/ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ 1.0 (sqrt x))
123.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
120.0ms	(/ 1.0 (sqrt (+ x 1.0)))
49.0ms	(/ 1.0 (sqrt x))
168.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.8s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	4935
1	1587
0	702

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
2.4b	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

1065×	`times-frac`
907×	`*-un-lft-identity`
781×	`add-sqr-sqrt`
721×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
76×	`distribute-lft-out`
56×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`log-prod` `flip3-+` `exp-sum` `flip-+`
22×	`fma-neg` `distribute-lft-out--`
18×	`difference-of-squares`
13×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`log-div` `exp-diff`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `frac-sub` `flip--`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 779

Calls

4 calls:

9.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
80.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
77.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
62.0ms	(/ 1.0 (sqrt x))
171.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
174.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

simplify1.8s

Counts

791 → 791

Iterations

Iter	Nodes
done	5000
2	4931
1	1674
0	763

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
2.3b	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))

rewrite726.0ms

Algorithm

rewrite-expression-head

Rules

2988×	`times-frac`
2506×	`*-un-lft-identity`
2131×	`add-sqr-sqrt`
2041×	`add-cube-cbrt`
1782×	`prod-diff`
1602×	`sqrt-prod`
207×	`distribute-lft-out`
156×	`div-inv`
132×	`sqrt-div` `associate-/r/`
66×	`flip3-+` `fma-neg` `flip-+`
33×	`distribute-lft-out--`
27×	`difference-of-squares`
11×	`add-log-exp`
7×	`pow-unpow`
6×	`pow1`
4×	`cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `unpow-prod-down` `pow-pow` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `log-pow` `sqr-pow`

Counts

4 → 1978

Calls

4 calls:

69.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
67.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
106.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
6.0ms	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))

series5.0s

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
131.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
4.6s	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))))

simplify983.0ms

Counts

1990 → 1990

Iterations

Iter	Nodes
done	5000
1	2287
0	887

prune5.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 19.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
13.1b	(- (/ (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (cbrt (sqrt x)))) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

55069×	`times-frac`
35996×	`cbrt-prod`
34884×	`*-un-lft-identity`
24804×	`add-sqr-sqrt`
24622×	`add-cube-cbrt`
20563×	`sqrt-prod`
18330×	`prod-diff`
5130×	`distribute-lft-out`
4222×	`div-inv`
1110×	`cbrt-div` `sqrt-div` `associate-/r/`
555×	`flip3-+` `flip-+`
40×	`difference-of-squares`
6×	`add-log-exp`
5×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 18439

Calls

4 calls:

1.0ms	(cbrt (sqrt x))
1.0ms	(cbrt (sqrt x))
1.0ms	(cbrt (sqrt x))
1.8s	(- (/ (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (cbrt (sqrt x)))) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (sqrt x))
141.0ms	(cbrt (sqrt x))
140.0ms	(cbrt (sqrt x))
164.0ms	(- (/ (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (cbrt (sqrt x)))) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

simplify8.6s

Counts

18451 → 18451

Iterations

Iter	Nodes
done	19266
0	19266

prune1.6m

Pruning

50 alts after pruning (50 fresh and 0 done)

Merged error: 19.9b

regimes1.1s

Accuracy

93.2% (0.5b remaining)

Error of 19.4b against oracle of 18.9b and baseline of 25.7b

bsearch53.0ms

Steps

Iters	Range		Point
6	7.901599787374112e+100	9.742269313565425e+101	2.6683734939066224e+101

simplify4.0ms

Iterations

Iter	Nodes
done	45
1	45
0	37

end0.0ms

sample1.3s

Algorithm

intervals

Results

293.0ms	1794×	body	640	valid
255.0ms	8020×	body	80	nan
193.0ms	1152×	body	1280	valid
156.0ms	4110×	body	80	valid
108.0ms	619×	body	320	valid
43.0ms	325×	body	160	valid