Details

analyze897.0ms (23.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	20×	body	80	invalid

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4982	11
1	4982	11

prune12.0ms (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: 1.1b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- z a))))
0.0b	(/ (- z t) (- z a))
1.7b	(* y (/ (- z t) (- z a)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 113

Calls

3 calls:

14.0ms	(* y (/ (- z t) (- z a)))
8.0ms	(/ (- z t) (- z a))
3.0ms	(+ x (* y (/ (- z t) (- z a))))

series53.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ x (* y (/ (- z t) (- z a))))
16.0ms	(* y (/ (- z t) (- z a)))
9.0ms	(/ (- z t) (- z a))

simplify39.0ms (1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4994	1366
1	4994	1366

prune168.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Merged error: 0b

Counts

123 → 6

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- z a)))))
0.0b	(/ 1 (- z a))
0.2b	(* (- z t) (/ 1 (- z a)))
1.7b	(* y (* (- z t) (/ 1 (- z a))))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 130

Calls

4 calls:

13.0ms	(* (- z t) (/ 1 (- z a)))
12.0ms	(* y (* (- z t) (/ 1 (- z a))))
5.0ms	(/ 1 (- z a))
4.0ms	(+ x (* y (* (- z t) (/ 1 (- z a)))))

series55.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (* y (* (- z t) (/ 1 (- z a)))))
16.0ms	(* y (* (- z t) (/ 1 (- z a))))
9.0ms	(* (- z t) (/ 1 (- z a)))
4.0ms	(/ 1 (- z a))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5082	1285

prune185.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Merged error: 0b

Counts

148 → 6

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ 1 (/ (- z a) (- z t)))))
0.0b	(/ (- z a) (- z t))
0.4b	(/ 1 (/ (- z a) (- z t)))
1.7b	(* y (/ 1 (/ (- z a) (- z t))))

rewrite77.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac`
336×	`add-sqr-sqrt`
324×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
82×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`flip3--` `flip--`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 338

Calls

4 calls:

30.0ms	(* y (/ 1 (/ (- z a) (- z t))))
12.0ms	(/ 1 (/ (- z a) (- z t)))
8.0ms	(/ (- z a) (- z t))
3.0ms	(+ x (* y (/ 1 (/ (- z a) (- z t)))))

series75.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ x (* y (/ 1 (/ (- z a) (- z t)))))
22.0ms	(* y (/ 1 (/ (- z a) (- z t))))
13.0ms	(/ 1 (/ (- z a) (- z t)))
9.0ms	(/ (- z a) (- z t))

simplify71.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5121	4569

prune639.0ms (16.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	349	1	350
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	351	5	356

Merged error: 0b

Counts

356 → 5

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ y (/ (- z a) (- z t))))
0.0b	(/ (- z a) (- z t))
2.0b	(/ y (/ (- z a) (- z t)))

rewrite62.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac`
197×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
6×	`flip3--` `flip--` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3-+` `div-sub` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 206

Calls

3 calls:

27.0ms	(+ x (/ y (/ (- z a) (- z t))))
12.0ms	(/ y (/ (- z a) (- z t)))
11.0ms	(/ (- z a) (- z t))

series61.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (/ y (/ (- z a) (- z t))))
22.0ms	(/ y (/ (- z a) (- z t)))
13.0ms	(/ (- z a) (- z t))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5338	3363

prune204.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	215	5	220

Merged error: 0b

Counts

220 → 5

regimes349.0ms (9%)

Accuracy

Total 0.9b remaining (97.6%)

Threshold costs 0.9b (97.6%)

bsearch36.0ms (0.9%)

Steps

Iters	Range		Point
8	5.0398721698197395e+22	1.1884374806127477e+27	5.14749771507477e+22
8	-3.36200802659743e-300	-8.914829840857724e-305	-3.273526225016458e-300

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	47
1	51	47

end0.0ms (0%)

sample590.0ms (15.2%)

Algorithm

1×

intervals

Results

298.0ms	8000×	body	80	valid
26.0ms	742×	body	80	invalid

Details

analyze897.0ms (23.1%)

sample23.0ms (0.6%)

simplify87.0ms (2.2%)

prune12.0ms (0.3%)

localize8.0ms (0.2%)

rewrite29.0ms (0.7%)

series53.0ms (1.4%)

simplify39.0ms (1%)

prune168.0ms (4.3%)

localize9.0ms (0.2%)

rewrite42.0ms (1.1%)

series55.0ms (1.4%)

simplify41.0ms (1.1%)

prune185.0ms (4.7%)

localize10.0ms (0.2%)

rewrite77.0ms (2%)

series75.0ms (1.9%)

simplify71.0ms (1.8%)

prune639.0ms (16.4%)

localize8.0ms (0.2%)

rewrite62.0ms (1.6%)

series61.0ms (1.6%)

simplify59.0ms (1.5%)

prune204.0ms (5.3%)

regimes349.0ms (9%)

bsearch36.0ms (0.9%)

simplify1.0ms (0%)

end0.0ms (0%)

sample590.0ms (15.2%)

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