Details

analyze2.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample9.0ms (0.7%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

valid

simplify25.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	345	5
1	345	5

prune4.0ms (0.3%)

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: 0.0b

Counts

2 → 1

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(/ x (- 1.0 x))

rewrite6.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
11×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv` `add-log-exp`

Counts

1 → 37

Calls

1 calls:

5.0ms

(/ x (- 1.0 x))

series3.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ x (- 1.0 x))

simplify55.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	368
1	4965	368

prune61.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Merged error: 0b

Counts

41 → 5

localize4.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(/ (- 1.0 x) x)
0.1b	(/ 1 (/ (- 1.0 x) x))

rewrite21.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac`
100×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `add-log-exp`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `flip--` `inv-pow`

Counts

2 → 138

Calls

2 calls:

7.0ms	(/ 1 (/ (- 1.0 x) x))
5.0ms	(/ (- 1.0 x) x)

series7.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (- 1.0 x) x)
3.0ms	(/ 1 (/ (- 1.0 x) x))

simplify71.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4925	1563
1	4925	1563

prune205.0ms (16.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	145	4	149

Merged error: 0b

Counts

149 → 4

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(- 1 (/ 1.0 x))
0.1b	(/ -1 (- 1 (/ 1.0 x)))

rewrite20.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
20×	`difference-of-squares`
15×	`add-cube-cbrt`
8×	`associate-/r*`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 65

Calls

2 calls:

9.0ms	(/ -1 (- 1 (/ 1.0 x)))
8.0ms	(- 1 (/ 1.0 x))

series5.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1 (/ 1.0 x))
3.0ms	(/ -1 (- 1 (/ 1.0 x)))

simplify45.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5358	819

prune115.0ms (9.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Merged error: 0b

Counts

75 → 4

localize6.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(/ x (- 1.0 x))
0.1b	(pow (/ x (- 1.0 x)) 3)
18.9b	(cbrt (pow (/ x (- 1.0 x)) 3))

rewrite26.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt` `*-un-lft-identity`
75×	`times-frac`
51×	`add-cube-cbrt`
48×	`cbrt-prod`
42×	`unpow-prod-down` `cube-prod`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube`
5×	`flip3--` `associate-/r*` `flip--` `div-inv`
4×	`pow1`
3×	`pow-unpow` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

3 → 157

Calls

3 calls:

8.0ms	(cbrt (pow (/ x (- 1.0 x)) 3))
7.0ms	(pow (/ x (- 1.0 x)) 3)
5.0ms	(/ x (- 1.0 x))

series10.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

4.0ms	(cbrt (pow (/ x (- 1.0 x)) 3))
3.0ms	(pow (/ x (- 1.0 x)) 3)
2.0ms	(/ x (- 1.0 x))

simplify35.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5639	1803

prune256.0ms (20.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	4	170

Merged error: 0b

Counts

170 → 4

regimes53.0ms (4.2%)

Accuracy

Total 0.0b remaining (77.2%)

Threshold costs 0.0b (77.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	5
1	14	5

end0.0ms (0%)

sample209.0ms (16.6%)

Algorithm

1×

intervals

Results

127.0ms

8000×

body

valid

Details

analyze2.0ms (0.2%)

sample9.0ms (0.7%)

simplify25.0ms (2%)

prune4.0ms (0.3%)

localize3.0ms (0.2%)

rewrite6.0ms (0.5%)

series3.0ms (0.2%)

simplify55.0ms (4.4%)

prune61.0ms (4.8%)

localize4.0ms (0.4%)

rewrite21.0ms (1.7%)

series7.0ms (0.6%)

simplify71.0ms (5.6%)

prune205.0ms (16.2%)

localize5.0ms (0.4%)

rewrite20.0ms (1.6%)

series5.0ms (0.4%)

simplify45.0ms (3.6%)

prune115.0ms (9.1%)

localize6.0ms (0.5%)

rewrite26.0ms (2.1%)

series10.0ms (0.8%)

simplify35.0ms (2.8%)

prune256.0ms (20.3%)

regimes53.0ms (4.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample209.0ms (16.6%)

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