Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	284×	body	80	nan
4.0ms	47×	body	640	valid
4.0ms	36×	body	1280	valid
4.0ms	141×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	8×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
87.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series253.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (sqrt x))
131.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.8s

Counts

748 → 748

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	691	40576
1	1510	35050
2	2953	26090
done	5000	20519

prune670.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 18.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1.0) (sqrt (sqrt x)))
0.2b	(/ (sqrt 1.0) (sqrt (sqrt x)))
0.3b	(* (+ (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
2.9b	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite4.4s

Algorithm

rewrite-expression-head

Rules

33597×	`sqrt-prod`
21654×	`times-frac`
16595×	`*-un-lft-identity`
14699×	`add-sqr-sqrt`
14285×	`add-cube-cbrt`
11484×	`prod-diff`
3830×	`distribute-rgt-in` `distribute-lft-in`
1102×	`distribute-lft-out`
696×	`sqrt-div`
381×	`div-inv`
348×	`associate-/r/`
178×	`flip3-+` `flip-+`
98×	`difference-of-squares`
86×	`associate-r`
68×	`distribute-lft-out--`
58×	`fma-neg`
37×	`associate-l`
18×	`associate-/r*`
12×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`flip3--` `frac-sub` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 11964

Calls

4 calls:

10.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
10.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
2.1s	(* (+ (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
303.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
174.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
575.0ms	(* (+ (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
286.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify4.2s

Counts

11976 → 11976

Iterations

Useful iterations: 0 (1.6s)

Iter	Nodes	Cost
0	5504	1202837
done	5504	1202837

prune31.9s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.2b	(/ (sqrt 1.0) (sqrt (sqrt x)))
0.3b	(* (+ (* (pow (/ 1 x) 1/4) (sqrt 1.0)) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
2.9b	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

33402×	`sqrt-prod`
21536×	`times-frac`
16466×	`*-un-lft-identity`
14630×	`add-sqr-sqrt`
14230×	`add-cube-cbrt`
11484×	`prod-diff`
3830×	`distribute-rgt-in` `distribute-lft-in`
1060×	`distribute-lft-out`
696×	`sqrt-div`
378×	`div-inv`
348×	`associate-/r/`
178×	`flip3-+` `flip-+`
98×	`difference-of-squares`
86×	`associate-r`
68×	`distribute-lft-out--`
58×	`fma-neg`
9×	`associate-/r*`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`frac-times` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `frac-sub` `flip--` `log1p-expm1-u`
3×	`sub-neg` `associate-r/` `associate-l*`
2×	`rem-sqrt-square` `pow1/2` `associate-*l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 11863

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
9.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
1.4s	(* (+ (* (pow (/ 1 x) 1/4) (sqrt 1.0)) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
286.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (sqrt x))
168.0ms	(/ (sqrt 1.0) (sqrt (sqrt x)))
523.0ms	(* (+ (* (pow (/ 1 x) 1/4) (sqrt 1.0)) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
266.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify4.0s

Counts

11875 → 11875

Iterations

Useful iterations: 0 (1.5s)

Iter	Nodes	Cost
0	5508	1231338
done	5508	1231338

prune34.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (* (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))))
2.9b	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
2.9b	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
2.9b	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite4.3s

Algorithm

rewrite-expression-head

Rules

33699×	`sqrt-prod`
21738×	`times-frac`
16585×	`*-un-lft-identity`
14869×	`add-sqr-sqrt`
14275×	`add-cube-cbrt`
11484×	`prod-diff`
1068×	`distribute-lft-out`
696×	`sqrt-div`
381×	`div-inv`
348×	`associate-/r/`
174×	`flip3-+` `fma-neg` `flip-+`
147×	`difference-of-squares`
102×	`distribute-lft-out--`
81×	`frac-times`
63×	`cbrt-div`
51×	`flip3--` `frac-sub` `flip--`
27×	`associate-*l/`
15×	`associate-*r/`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 12027

Calls

4 calls:

1.5s	(cbrt (* (* (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))))
282.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
281.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
288.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt (* (* (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))) (- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))))
257.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
256.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
256.0ms	(- (/ (sqrt 1.0) (sqrt (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify3.5s

Counts

12039 → 12039

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	2260	964793
1	4805	817530
done	5001	771369

prune14.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.1b

regimes121.0ms

Accuracy

97.9% (0.2b remaining)

Error of 10.1b against oracle of 9.9b and baseline of 19.6b

bsearch51.0ms

Steps

Iters	Range		Point
8	211.08706756948936	1126179.5725289274	7248.001864012984

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	74
1	54	74
done	54	74

end0.0ms

sample843.0ms

Algorithm

intervals

Results

160.0ms	8130×	body	80	nan
157.0ms	1787×	body	640	valid
130.0ms	1123×	body	1280	valid
103.0ms	4167×	body	80	valid
41.0ms	623×	body	320	valid
15.0ms	300×	body	160	valid