Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample29.0ms (1%)

Algorithm

1×

intervals

Results

10.0ms	73×	body	640	valid
6.0ms	31×	body	1280	valid
5.0ms	125×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 21.4b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite51.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 116

Calls

3 calls:

36.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))

series26.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
7.0ms	(/ 1.0 (sqrt x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))

simplify33.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5082	1654

prune297.0ms (10.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	12	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 20.8b

Counts

126 → 12

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
2.7b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite38.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 76

Calls

3 calls:

19.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series46.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4987	1388
1	4987	1388

prune210.0ms (7.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Merged error: 0.3b

Counts

97 → 8

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite56.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative`

Counts

4 → 125

Calls

4 calls:

23.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))

series59.0ms (2%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
5.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5523	2087

prune355.0ms (12.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 0.0b

Counts

145 → 11

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

rewrite35.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac`
72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
55×	`sqrt-prod`
48×	`add-cube-cbrt`
23×	`distribute-lft-out`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r` `associate-/l`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

12.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
3.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))

series50.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
10.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	4295
1	4975	4295

prune495.0ms (17%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	190	9	199

Merged error: 0b

Counts

199 → 9

regimes54.0ms (1.9%)

Accuracy

Total 0.3b remaining (85.1%)

Threshold costs 0.3b (85.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms (0%)

sample832.0ms (28.7%)

Algorithm

1×

intervals

Results

279.0ms	1889×	body	640	valid
213.0ms	1140×	body	1280	valid
150.0ms	3991×	body	80	valid
70.0ms	639×	body	320	valid
24.0ms	341×	body	160	valid

Details

analyze1.0ms (0%)

sample29.0ms (1%)

simplify11.0ms (0.4%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

rewrite51.0ms (1.7%)

series26.0ms (0.9%)

simplify33.0ms (1.1%)

prune297.0ms (10.2%)

localize8.0ms (0.3%)

rewrite38.0ms (1.3%)

series46.0ms (1.6%)

simplify33.0ms (1.2%)

prune210.0ms (7.2%)

localize11.0ms (0.4%)

rewrite56.0ms (1.9%)

series59.0ms (2%)

simplify59.0ms (2%)

prune355.0ms (12.2%)

localize14.0ms (0.5%)

rewrite35.0ms (1.2%)

series50.0ms (1.7%)

simplify83.0ms (2.8%)

prune495.0ms (17%)

regimes54.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample832.0ms (28.7%)

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