Details

sample53.0ms

Algorithm

intervals

Results

13.0ms	62×	body	640	valid
9.0ms	211×	body	80	nan
9.0ms	39×	body	1280	valid
7.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

13.0ms	(sqrt (+ x 1))
27.0ms	(/ 1 (sqrt (+ x 1)))
13.0ms	(/ 1 (sqrt x))
91.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1))
49.0ms	(/ 1 (sqrt (+ x 1)))
31.0ms	(/ 1 (sqrt x))
106.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.5s

Counts

179 → 179

Iterations

Iter	Nodes
done	5057
4	4762
3	2343
2	988
1	407
0	208

prune601.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
2.6b	(exp (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

189×	`add-sqr-sqrt`
155×	`times-frac`
147×	`*-un-lft-identity`
92×	`sqrt-prod`
50×	`difference-of-squares`
49×	`add-cube-cbrt`
41×	`log-prod` `exp-sum`
26×	`distribute-lft-out--`
13×	`associate-/r*`
12×	`add-exp-log`
10×	`div-inv` `distribute-lft-out`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`exp-prod` `div-exp` `insert-posit16`
3×	`log-div` `exp-diff`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `frac-sub` `flip--` `inv-pow`
1×	`sub-neg` `flip3-+` `diff-log` `log-pow` `flip-+` `rem-exp-log`

Counts

4 → 207

Calls

4 calls:

25.0ms	(/ 1 (sqrt (+ x 1)))
13.0ms	(/ 1 (sqrt x))
86.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
54.0ms	(exp (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (sqrt (+ x 1)))
29.0ms	(/ 1 (sqrt x))
74.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
78.0ms	(exp (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

simplify3.0s

Counts

219 → 219

Iterations

Iter	Nodes
done	5002
4	4853
3	2575
2	1045
1	490
0	282

prune747.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
8.8b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`times-frac`
26×	`sqrt-prod`
20×	`add-cube-cbrt`
15×	`difference-of-squares`
7×	`associate-/r*` `add-exp-log`
6×	`pow1`
5×	`unpow-prod-down` `add-cbrt-cube` `distribute-lft-out` `add-log-exp` `sqr-pow`
4×	`sqrt-div`
3×	`insert-posit16` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `associate-/r/` `flip-+` `div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

3 → 99

Calls

3 calls:

15.0ms	(sqrt (+ x 1))
22.0ms	(/ 1 (sqrt (+ x 1)))
57.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series158.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(sqrt (+ x 1))
39.0ms	(/ 1 (sqrt (+ x 1)))
78.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
3	2291
2	872
1	363
0	173

prune384.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.0b

localize70.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
2.5b	(pow (exp (* (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

235×	`add-sqr-sqrt`
174×	`times-frac`
160×	`*-un-lft-identity`
96×	`sqrt-prod`
75×	`difference-of-squares`
39×	`distribute-lft-out--`
25×	`add-cube-cbrt`
12×	`div-inv`
11×	`add-log-exp`
9×	`distribute-lft-out`
7×	`pow-unpow`
6×	`pow1`
4×	`cbrt-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16`
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 → 180

Calls

4 calls:

75.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
56.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
73.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms	(pow (exp (* (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
86.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
102.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.8s	(pow (exp (* (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))

simplify3.1s

Counts

192 → 192

Iterations

Iter	Nodes
done	5006
2	3093
1	762
0	258

prune806.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.0b

regimes87.0ms

Accuracy

94.5% (0.4b remaining)

Error of 19.7b against oracle of 19.3b and baseline of 26.3b

bsearch70.0ms

Steps

Iters	Range		Point
7	3.974905491533812e+107	3.1637000559480493e+109	5.2088959942045496e+107

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample2.1s

Algorithm

intervals

Results

479.0ms	1873×	body	640	valid
410.0ms	7974×	body	80	nan
403.0ms	619×	body	320	valid
348.0ms	1119×	body	1280	valid
256.0ms	4064×	body	80	valid
32.0ms	325×	body	160	valid