Details

analyze960.0ms (25.6%)

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
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	23×	body	80	invalid

simplify120.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4900	11
1	4900	11

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 10.6b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(- t (* a z))
0.0b	(- x (* y z))
10.3b	(/ (- x (* y z)) (- t (* a z)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3--` `flip--`
3×	`pow1` `associate-/r` `associate-/l`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 54

Calls

3 calls:

6.0ms	(/ (- x (* y z)) (- t (* a z)))
3.0ms	(- x (* y z))
3.0ms	(- t (* a z))

series37.0ms (1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (- x (* y z)) (- t (* a z)))
10.0ms	(- t (* a z))
7.0ms	(- x (* y z))

simplify44.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5502	755

prune123.0ms (3.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	11	64

Merged error: 6.1b

Counts

64 → 11

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- t (* z a))
2.6b	(/ x (- t (* z a)))
3.4b	(* y (/ z (- t (* z a))))
7.8b	(/ z (- t (* z a)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

8.0ms	(* y (/ z (- t (* z a))))
4.0ms	(/ z (- t (* z a)))
4.0ms	(/ x (- t (* z a)))
3.0ms	(- t (* z a))

series44.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* y (/ z (- t (* z a))))
13.0ms	(/ x (- t (* z a)))
11.0ms	(/ z (- t (* z a)))
6.0ms	(- t (* z a))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5204	1123

prune173.0ms (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	116	10	126

Merged error: 1.8b

Counts

126 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (- t (* z a))) (pow (/ y (- (/ t z) a)) 1))
0.0b	(- t (* z a))
2.6b	(/ x (- t (* z a)))
3.5b	(/ y (- (/ t z) a))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
37×	`times-frac`
33×	`*-un-lft-identity`
23×	`add-cube-cbrt`
16×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`distribute-lft-out--`
4×	`pow1` `unpow-prod-down` `flip3--` `associate-/r/` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

32.0ms	(- (/ x (- t (* z a))) (pow (/ y (- (/ t z) a)) 1))
8.0ms	(/ y (- (/ t z) a))
4.0ms	(/ x (- t (* z a)))
3.0ms	(- t (* z a))

series73.0ms (2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ x (- t (* z a))) (pow (/ y (- (/ t z) a)) 1))
20.0ms	(/ x (- t (* z a)))
12.0ms	(/ y (- (/ t z) a))
11.0ms	(- t (* z a))

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4932	1516
1	4932	1516

prune175.0ms (4.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	113	10	123

Merged error: 1.8b

Counts

123 → 10

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (- t (* z a))) (pow (/ 1 (/ (- (/ t z) a) y)) 1))
1.0b	(/ 1 (/ (- (/ t z) a) y))
2.6b	(/ x (- t (* z a)))
3.4b	(/ (- (/ t z) a) y)

rewrite98.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

207×	`add-sqr-sqrt`
200×	`times-frac`
124×	`*-un-lft-identity`
86×	`add-cube-cbrt`
46×	`difference-of-squares`
28×	`associate-/r*`
19×	`add-exp-log`
17×	`distribute-lft-out--`
13×	`add-cbrt-cube`
12×	`associate-/l*`
10×	`unpow-prod-down`
9×	`div-exp`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
2×	`rec-exp` `1-exp` `associate-/l/` `sqr-pow`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `inv-pow`

Counts

4 → 209

Calls

4 calls:

63.0ms	(- (/ x (- t (* z a))) (pow (/ 1 (/ (- (/ t z) a) y)) 1))
12.0ms	(/ 1 (/ (- (/ t z) a) y))
9.0ms	(/ (- (/ t z) a) y)
4.0ms	(/ x (- t (* z a)))

series70.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (/ (- (/ t z) a) y))
24.0ms	(- (/ x (- t (* z a))) (pow (/ 1 (/ (- (/ t z) a) y)) 1))
11.0ms	(/ x (- t (* z a)))
10.0ms	(/ (- (/ t z) a) y)

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5301	3377

prune280.0ms (7.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	221	10	231

Merged error: 1.8b

Counts

231 → 10

regimes561.0ms (15%)

Accuracy

Total 0.1b remaining (6%)

Threshold costs 0.1b (6%)

bsearch37.0ms (1%)

Steps

Iters	Range		Point
7	18871229608190304.0	4.45669092387865e+17	2.045405544225239e+16
8	-4.375031376331144e-55	-1.3006420217584113e-57	-3.490398922392778e-57

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	35
1	83	35

end0.0ms (0%)

sample624.0ms (16.6%)

Algorithm

1×

intervals

Results

316.0ms	8000×	body	80	valid
27.0ms	734×	body	80	invalid

Details

analyze960.0ms (25.6%)

sample24.0ms (0.6%)

simplify120.0ms (3.2%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite13.0ms (0.3%)

series37.0ms (1%)

simplify44.0ms (1.2%)

prune123.0ms (3.3%)

localize9.0ms (0.2%)

rewrite22.0ms (0.6%)

series44.0ms (1.2%)

simplify55.0ms (1.5%)

prune173.0ms (4.6%)

localize12.0ms (0.3%)

rewrite50.0ms (1.3%)

series73.0ms (2%)

simplify52.0ms (1.4%)

prune175.0ms (4.7%)

localize16.0ms (0.4%)

rewrite98.0ms (2.6%)

series70.0ms (1.9%)

simplify58.0ms (1.6%)

prune280.0ms (7.5%)

regimes561.0ms (15%)

bsearch37.0ms (1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample624.0ms (16.6%)

Profiling