Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

Calls

3 calls:

7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))

series29.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune148.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
7.3b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
46×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`pow1` `cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`cbrt-div` `flip3-+` `sqrt-prod` `flip-+` `add-log-exp`
3×	`pow-unpow` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 153

Calls

4 calls:

10.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
7.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
6.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))
3.0ms	(sqrt (+ x 1.0))

series40.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
14.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
5.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))
4.0ms	(sqrt (+ x 1.0))

simplify92.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5113	2594

prune402.0ms (12.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	165	5	170

Merged error: 0b

Counts

170 → 5

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt x) (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite67.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `flip3-+` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
6×	`times-frac` `sqrt-prod` `associate-/l*`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

32.0ms	(/ (sqrt x) (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
10.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
10.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
10.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series977.0ms (29.8%)

Counts

4 → 12

Calls

4 calls:

896.0ms	(/ (sqrt x) (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
36.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
25.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
20.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5169	3599

prune518.0ms (15.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Merged error: 0b

Counts

94 → 5

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(log (/ x (+ 1.0 (sqrt (+ x 1.0)))))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
3.7b	(exp (log (/ x (+ 1.0 (sqrt (+ x 1.0))))))

rewrite30.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity`
36×	`log-prod` `times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`exp-sum`
11×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `associate-/r/` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3-+` `associate-/r*` `flip-+`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `exp-diff` `clear-num` `sum-log` `rem-exp-log`

Counts

4 → 105

Calls

4 calls:

8.0ms	(exp (log (/ x (+ 1.0 (sqrt (+ x 1.0))))))
7.0ms	(log (/ x (+ 1.0 (sqrt (+ x 1.0)))))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))

series78.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (/ x (+ 1.0 (sqrt (+ x 1.0)))))
18.0ms	(exp (log (/ x (+ 1.0 (sqrt (+ x 1.0))))))
15.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4967	2646
1	4967	2646

prune302.0ms (9.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	117	5	122

Merged error: 0b

Counts

122 → 5

regimes76.0ms (2.3%)

Accuracy

Total 0.2b remaining (95%)

Threshold costs 0.2b (95%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms (0%)

sample300.0ms (9.2%)

Algorithm

1×

intervals

Results

213.0ms	7998×	body	80	valid
0.0ms	2×	body	1280	valid

Details

analyze3.0ms (0.1%)

sample12.0ms (0.4%)

simplify3.0ms (0.1%)

prune5.0ms (0.1%)

localize5.0ms (0.2%)

rewrite17.0ms (0.5%)

series29.0ms (0.9%)

simplify24.0ms (0.7%)

prune148.0ms (4.5%)

localize8.0ms (0.3%)

rewrite31.0ms (1%)

series40.0ms (1.2%)

simplify92.0ms (2.8%)

prune402.0ms (12.3%)

localize16.0ms (0.5%)

rewrite67.0ms (2%)

series977.0ms (29.8%)

simplify34.0ms (1%)

prune518.0ms (15.8%)

localize9.0ms (0.3%)

rewrite30.0ms (0.9%)

series78.0ms (2.4%)

simplify55.0ms (1.7%)

prune302.0ms (9.2%)

regimes76.0ms (2.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample300.0ms (9.2%)

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