Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	284×	body	80	nan
4.0ms	51×	body	1280	valid
3.0ms	141×	body	80	valid
2.0ms	31×	body	640	valid
1.0ms	25×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize5.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

52.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts

73 → 73

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	117	1805
1	254	1268
2	569	970
3	1667	800
done	5000	698

prune84.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
23×	`sqrt-prod`
20×	`distribute-lft-out`
18×	`times-frac`
15×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`fma-def` `associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 65

Calls

2 calls:

22.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
36.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series204.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
137.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	132	983
1	313	898
2	848	818
3	2615	805
done	5001	804

prune153.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series772.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (cbrt x) (cbrt x))
186.0ms	(cbrt x)
192.0ms	(cbrt x)
186.0ms	(cbrt x)

simplify3.7s

Counts

93 → 93

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune274.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.1b	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.3b	(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity`
165×	`sqrt-prod`
130×	`times-frac`
128×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
60×	`distribute-lft-out`
33×	`associate-r` `associate-l`
32×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `hypot-def` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 247

Calls

4 calls:

37.0ms	(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
40.0ms	(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
37.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
181.0ms	(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))

series882.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
261.0ms	(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
324.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
137.0ms	(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.3s

Counts

259 → 259

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	335	5744
1	872	5003
2	2492	4217
done	5000	4169

prune454.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

end0.0ms

sample730.0ms

Algorithm

intervals

Results

142.0ms	1699×	body	1280	valid
142.0ms	8130×	body	80	nan
81.0ms	1207×	body	640	valid
79.0ms	4169×	body	80	valid
29.0ms	617×	body	320	valid
10.0ms	308×	body	160	valid