Details

analyze1.2s (21.4%)

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
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
26.2%	73.6%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample73.0ms (1.4%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify114.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series60.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

38.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
22.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune92.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	4	140

Error

0.0b

Counts

140 → 4

Alt Table

Status	Error	Program
▶	1.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	2.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	23.3b	(fma.f64 y (fma.f64 -1 (/.f64 z t) 1) x)

Compiler

Compiled 3307 to 1100 computations (66.7% saved)

localize37.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	8.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series102.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

48.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
35.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
19.0ms	(/.f64 y (-.f64 a t))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

11.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
4.0ms	(/.f64 y (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

simplify267.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune201.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	307	5	312

Error

Counts

312 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	23.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))))
✓	2.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	23.3b	(fma.f64 y (fma.f64 -1 (/.f64 z t) 1) x)

Compiler

Compiled 8035 to 2066 computations (74.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	12.2b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series92.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

47.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
37.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
7.0ms	(*.f64 y (-.f64 z t))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 98

Calls

3 calls:

9.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
7.0ms	(*.f64 y (-.f64 z t))
6.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

simplify182.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

426×	`sub-neg_binary64`
348×	`div-sub_binary64`
330×	`fma-neg_binary64`
239×	`associate-/l*_binary64`
225×	`associate--l+_binary64`

Counts

242 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	5059
1	885	4624
2	3750	4528
3	4597	4524
4	5233	4524

prune129.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
▶	23.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))))
✓	2.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	23.3b	(fma.f64 y (fma.f64 -1 (/.f64 z t) 1) x)

Compiler

Compiled 5367 to 1557 computations (71% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a t))
✓	0.3b	(.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))))
✓	4.0b	(sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	8.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series572.0ms (10.5%)

Counts

2 → 56

Calls

2 calls:

299.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))))
272.0ms	(sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`sqrt-div_binary64`
54×	`pow1_binary64`
51×	`frac-times_binary64`
31×	`associate-*r/_binary64`
30×	`sqrt-pow1_binary64`

Counts

2 → 104

Calls

2 calls:

18.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))))
9.0ms	(sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

simplify138.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

538×	`times-frac_binary64`
383×	`associate-/l*_binary64`
328×	`associate-l_binary64`
328×	`associate-/r*_binary64`
279×	`fma-def_binary64`

Counts

160 → 209

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	6218
1	1417	6004
2	5000	6004
3	4985	6004

prune419.0ms (7.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	675	0	675
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	675	5	680

Error

Counts

680 → 5

Alt Table

Status	Error	Program
✓	1.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	23.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) (sqrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))))
✓	2.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	12.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	23.3b	(fma.f64 y (fma.f64 -1 (/.f64 z t) 1) x)

Compiler

Compiled 28094 to 7123 computations (74.6% saved)

regimes626.0ms (11.5%)

Accuracy

Total 1.1b remaining (98.5%)

Threshold costs 0b (0%)

Counts

62 → 3

Compiler

Compiled 8066 to 4930 computations (38.9% saved)

bsearch40.0ms (0.7%)

Steps

Iters	Range		Point
8	5.9896097072577275e+180	1.702376440395059e+185	1.9758692242271444e+183
8	-5.284126285581088e+146	-1.3924214477710296e+143	-1.2069852408039634e+146

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	25	42
2	31	42
3	33	42
4	34	42
5	34	42

end1.0ms (0%)

Compiler: Compiled 34 to 18 computations (47.1% saved)

sample848.0ms (15.6%)

Algorithm

1×

intervals

Results

382.0ms	8000×	body	128	valid
43.0ms	739×	body	128	invalid

Compiler

Compiled 145 to 85 computations (41.4% saved)

Details

analyze1.2s (21.4%)

sample73.0ms (1.4%)

simplify114.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series60.0ms (1.1%)

rewrite14.0ms (0.3%)

simplify117.0ms (2.1%)

prune92.0ms (1.7%)

localize37.0ms (0.7%)

series102.0ms (1.9%)

rewrite33.0ms (0.6%)

simplify267.0ms (4.9%)

prune201.0ms (3.7%)

localize8.0ms (0.1%)

series92.0ms (1.7%)

rewrite28.0ms (0.5%)

simplify182.0ms (3.4%)

prune129.0ms (2.4%)

localize10.0ms (0.2%)

series572.0ms (10.5%)

rewrite42.0ms (0.8%)

simplify138.0ms (2.5%)

prune419.0ms (7.7%)

regimes626.0ms (11.5%)

bsearch40.0ms (0.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample848.0ms (15.6%)

Profiling