Details

analyze1.1s (24.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

sample32.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	103×	body	80	invalid

simplify295.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (293.0ms)

Iter	Nodes	Cost
0	4888	13
1	4888	13

prune13.0ms (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: 6.1b

Counts

2 → 2

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(* (* z 9.0) t)
0.2b	(- (* x y) (* (* z 9.0) t))
5.7b	(/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

3 → 53

Calls

3 calls:

7.0ms	(/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
5.0ms	(* (* z 9.0) t)
4.0ms	(- (* x y) (* (* z 9.0) t))

series39.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
12.0ms	(- (* x y) (* (* z 9.0) t))
3.0ms	(* (* z 9.0) t)

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5095	704

prune127.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	9	64

Merged error: 0.0b

Counts

64 → 9

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* z (* 9.0 t))
0.2b	(- (* x y) (* z (* 9.0 t)))
0.6b	(/ 1 (* 2.0 (/ a (- (* x y) (* z (* 9.0 t))))))
5.7b	(/ a (- (* x y) (* z (* 9.0 t))))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `times-frac`
10×	`div-exp`
9×	`prod-exp`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`pow-prod-down` `associate-/r*`
3×	`rec-exp` `1-exp` `associate-l` `associate-/r/`
2×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `associate-r/` `associate-r` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

9.0ms	(/ 1 (* 2.0 (/ a (- (* x y) (* z (* 9.0 t))))))
6.0ms	(- (* x y) (* z (* 9.0 t)))
6.0ms	(/ a (- (* x y) (* z (* 9.0 t))))
5.0ms	(* z (* 9.0 t))

series59.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (* 2.0 (/ a (- (* x y) (* z (* 9.0 t))))))
17.0ms	(/ a (- (* x y) (* z (* 9.0 t))))
12.0ms	(- (* x y) (* z (* 9.0 t)))
3.0ms	(* z (* 9.0 t))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4979	1260
1	4979	1260

prune187.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (* y (/ x (* a 2.0))) (* t (* (/ z a) (/ 9.0 2.0))))
0.2b	(* (/ z a) (/ 9.0 2.0))
5.0b	(* t (* (/ z a) (/ 9.0 2.0)))
5.1b	(* y (/ x (* a 2.0)))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-exp-log` `add-cbrt-cube`
36×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`associate-r`
19×	`associate-l`
17×	`prod-exp` `cbrt-unprod`
15×	`associate-*r/`
13×	`pow1`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow-prod-down` `unswap-sqr`
4×	`frac-times`
3×	`associate-l/` `-commutative` `frac-sub` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `sub-div`

Counts

4 → 119

Calls

4 calls:

10.0ms	(* (/ z a) (/ 9.0 2.0))
8.0ms	(* t (* (/ z a) (/ 9.0 2.0)))
8.0ms	(- (* y (/ x (* a 2.0))) (* t (* (/ z a) (/ 9.0 2.0))))
7.0ms	(* y (/ x (* a 2.0)))

series40.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (* y (/ x (* a 2.0))) (* t (* (/ z a) (/ 9.0 2.0))))
6.0ms	(* y (/ x (* a 2.0)))
6.0ms	(* t (* (/ z a) (/ 9.0 2.0)))
5.0ms	(* (/ z a) (/ 9.0 2.0))

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	1382
1	4981	1382

prune243.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	130	11	141

Merged error: 0.0b

Counts

141 → 11

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (* (/ y a) (/ x 2.0)) (* t (* (/ z a) (/ 9.0 2.0))))
0.2b	(* (/ z a) (/ 9.0 2.0))
5.0b	(* t (* (/ z a) (/ 9.0 2.0)))
5.2b	(* (/ y a) (/ x 2.0))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
46×	`add-exp-log` `add-cbrt-cube`
44×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-l`
27×	`associate-r`
26×	`associate-*r/`
17×	`prod-exp` `cbrt-unprod`
13×	`pow1`
12×	`cbrt-undiv` `div-exp`
11×	`frac-times` `associate-*l/`
9×	`frac-sub`
8×	`unswap-sqr`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`div-inv`
3×	`*-commutative` `sub-div`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 150

Calls

4 calls:

10.0ms	(* (/ z a) (/ 9.0 2.0))
10.0ms	(* (/ y a) (/ x 2.0))
9.0ms	(- (* (/ y a) (/ x 2.0)) (* t (* (/ z a) (/ 9.0 2.0))))
8.0ms	(* t (* (/ z a) (/ 9.0 2.0)))

series40.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (* (/ y a) (/ x 2.0)) (* t (* (/ z a) (/ 9.0 2.0))))
7.0ms	(* (/ y a) (/ x 2.0))
6.0ms	(* t (* (/ z a) (/ 9.0 2.0)))
3.0ms	(* (/ z a) (/ 9.0 2.0))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4985	1747
1	4985	1747

prune239.0ms (5.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	162	11	173

Merged error: 0.0b

Counts

173 → 11

regimes927.0ms (20%)

Accuracy

Total 5.9b remaining (99.4%)

Threshold costs 0b (0%)

bsearch37.0ms (0.8%)

Steps

Iters	Range		Point
6	7.787982571490603e+134	9.378240345624404e+135	1.1206573610708866e+135
7	-5.068930411181156e-33	-2.228908441178274e-35	-4.175740189811104e-35

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	146	57
1	146	57

end0.0ms (0%)

sample844.0ms (18.2%)

Algorithm

1×

intervals

Results

349.0ms	8000×	body	80	valid
138.0ms	3121×	body	80	invalid

Details

analyze1.1s (24.6%)

sample32.0ms (0.7%)

simplify295.0ms (6.4%)

prune13.0ms (0.3%)

localize10.0ms (0.2%)

rewrite17.0ms (0.4%)

series39.0ms (0.8%)

simplify33.0ms (0.7%)

prune127.0ms (2.7%)

localize12.0ms (0.3%)

rewrite28.0ms (0.6%)

series59.0ms (1.3%)

simplify62.0ms (1.3%)

prune187.0ms (4%)

localize12.0ms (0.3%)

rewrite38.0ms (0.8%)

series40.0ms (0.9%)

simplify58.0ms (1.2%)

prune243.0ms (5.2%)

localize15.0ms (0.3%)

rewrite43.0ms (0.9%)

series40.0ms (0.9%)

simplify49.0ms (1.1%)

prune239.0ms (5.2%)

regimes927.0ms (20%)

bsearch37.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample844.0ms (18.2%)

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