Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

valid

simplify68.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4970	14
1	4970	14

prune8.0ms (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 → 2

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.0b	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

rewrite31.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 105

Calls

3 calls:

14.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

series20.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

simplify43.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5591	1958

prune221.0ms (8.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	110	6	116

Merged error: 0b

Counts

116 → 6

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(log (pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0))
0.0b	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
1.3b	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)

rewrite46.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
60×	`times-frac`
52×	`exp-prod`
39×	`add-cube-cbrt`
27×	`pow-pow`
16×	`distribute-lft-out`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log` `log-prod`
6×	`unpow-prod-down` `associate-/r/` `add-cbrt-cube`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*`
3×	`pow-unpow` `flip3-+` `rem-log-exp` `flip-+` `div-inv`
2×	`pow-to-exp` `div-sub` `pow-exp` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log-pow` `flip--` `rem-exp-log`

Counts

4 → 142

Calls

4 calls:

13.0ms	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)
9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
9.0ms	(log (pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series55.0ms (2%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)
17.0ms	(log (pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0))
10.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4992	3004
1	4992	3004

prune396.0ms (14.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	155	5	160

Merged error: 0b

Counts

160 → 5

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
0.0b	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
0.0b	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

rewrite73.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

322×	`times-frac`
292×	`*-un-lft-identity`
220×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
83×	`associate-r`
42×	`distribute-lft-out`
36×	`add-exp-log`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`pow1` `cbrt-undiv` `prod-exp` `associate-/l*`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`associate-l` `sum-log` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 299

Calls

4 calls:

30.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
12.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))
9.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

series30.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
7.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))
7.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

simplify93.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4954	5899
1	4954	5899

prune784.0ms (28.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	311	5	316

Merged error: 0b

Counts

316 → 5

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.0b	(* (/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x))))) (- x 1.0))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out` `add-log-exp`
5×	`pow1` `associate-r`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `sum-log` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-*r/` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `associate-+r+` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 92

Calls

3 calls:

15.0ms	(* (/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x))))) (- x 1.0))
6.0ms	(/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))
5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

series18.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(* (/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x))))) (- x 1.0))
6.0ms	(/ 6.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))

simplify48.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4990	1700
1	4990	1700

prune188.0ms (6.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	101	5	106

Merged error: 0b

Counts

106 → 5

regimes36.0ms (1.3%)

Accuracy

Total 0.0b remaining (77.2%)

Threshold costs 0.0b (77.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	16
1	26	16

end0.0ms (0%)

sample417.0ms (15.3%)

Algorithm

1×

intervals

Results

323.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

analyze3.0ms (0.1%)

sample20.0ms (0.7%)

simplify68.0ms (2.5%)

prune8.0ms (0.3%)

localize9.0ms (0.3%)

rewrite31.0ms (1.1%)

series20.0ms (0.7%)

simplify43.0ms (1.6%)

prune221.0ms (8.1%)

localize14.0ms (0.5%)

rewrite46.0ms (1.7%)

series55.0ms (2%)

simplify58.0ms (2.1%)

prune396.0ms (14.5%)

localize10.0ms (0.4%)

rewrite73.0ms (2.7%)

series30.0ms (1.1%)

simplify93.0ms (3.4%)

prune784.0ms (28.7%)

localize9.0ms (0.3%)

rewrite29.0ms (1.1%)

series18.0ms (0.7%)

simplify48.0ms (1.8%)

prune188.0ms (6.9%)

regimes36.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample417.0ms (15.3%)

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