Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	61×	body	1280	valid
6.0ms	245×	body	80	nan
3.0ms	135×	body	80	valid
3.0ms	37×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	10×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite72.0ms

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:

67.0ms

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

series89.0ms

Counts

1 → 3

Calls

1 calls:

89.0ms

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

simplify2.7s

Counts

73 → 73

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	117	1805
1	265	1282
2	827	970
3	4251	800
done	5000	799

prune253.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

24.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
79.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series264.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
182.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify920.0ms

Counts

80 → 80

Iterations

Useful iterations: done (916.0ms)

Iter	Nodes	Cost
0	143	1265
1	368	1016
2	1620	938
done	5001	931

prune393.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.0b	(log1p (expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
0.1b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.5b	(expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))

rewrite99.0ms

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×	`log1p-expm1-u`
4×	`pow1` `expm1-log1p-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:

31.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
0.0ms	(log1p (expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
64.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
1.0ms	(expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
764.0ms	(log1p (expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
168.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
365.0ms	(expm1 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	200	1558
1	517	1431
2	2196	1278
done	5000	1273

prune496.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (expm1 (log1p (/ 1.0 (+ (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))))
0.5b	(expm1 (expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

0.0ms	(log1p (expm1 (expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))))
0.0ms	(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
46.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
1.0ms	(expm1 (expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))))

series6.5s

Counts

4 → 12

Calls

4 calls:

3.1s	(log1p (expm1 (expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))))
1.2s	(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
202.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
1.9s	(expm1 (expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))))

simplify2.3s

Counts

88 → 88

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	283	2206
1	829	1969
2	3838	1767
done	5000	1740

prune585.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	13	13
done	13	13

end0.0ms

sample2.2s

Algorithm

intervals

Results

868.0ms	7921×	body	80	nan
387.0ms	1664×	body	1280	valid
261.0ms	1273×	body	640	valid
192.0ms	4141×	body	80	valid
67.0ms	611×	body	320	valid
22.0ms	311×	body	160	valid