Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	54×	body	1280	valid
4.0ms	237×	body	80	nan
3.0ms	45×	body	640	valid
2.0ms	134×	body	80	valid
1.0ms	12×	body	320	valid
0.0ms	11×	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: 28.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
51.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series97.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (+ x 1.0))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts

95 → 95

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	137	1993
1	301	1432
2	677	1124
3	1959	950
done	5000	846

prune124.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
19.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series237.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
69.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
139.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.4s

Counts

93 → 93

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	158	1171
1	364	1060
2	967	972
3	2933	955
done	5000	954

prune204.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.0b	(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
0.1b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
20.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
0.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
39.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

464.0ms	(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
61.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
806.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
139.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify913.0ms

Counts

99 → 99

Iterations

Useful iterations: done (910.0ms)

Iter	Nodes	Cost
0	227	1784
1	578	1630
2	1841	1446
done	5001	1363

prune269.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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:

12.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series769.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (cbrt x) (cbrt x))
191.0ms	(cbrt x)
188.0ms	(cbrt x)
187.0ms	(cbrt x)

simplify3.4s

Counts

93 → 93

Iterations

Useful iterations: done (3.4s)

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

prune310.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
done	11	11

end0.0ms

sample679.0ms

Algorithm

intervals

Results

140.0ms	1688×	body	1280	valid
132.0ms	7989×	body	80	nan
78.0ms	1192×	body	640	valid
71.0ms	4145×	body	80	valid
31.0ms	656×	body	320	valid
10.0ms	319×	body	160	valid