Details

analyze826.0ms (12.4%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.3s (19.5%)

Results

1.1s	8256×	body	128	valid
81.0ms	505×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

26.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 71 to 35 computations (50.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 b c) (.f64 a d))
✓	25.6b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series103.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

94.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

443×	`fma-def_binary64`
380×	`times-frac_binary64`
343×	`associate-/l*_binary64`
339×	`fma-neg_binary64`
229×	`associate-*l/_binary64`

Counts

146 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	2770
1	373	2658
2	1299	2612
3	4668	2596
4	4941	2596

prune78.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Error

1.2b

Counts

114 → 10

Alt Table

Status	Error	Program
	41.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c)))
	46.2b	(exp.f64 (-.f64 (log.f64 (-.f64 (.f64 b c) (.f64 a d))) (log.f64 (+.f64 (.f64 c c) (.f64 d d)))))
	35.4b	(neg.f64 (/.f64 a d))
✓	26.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
	26.2b	(/.f64 1 (/.f64 (fma.f64 d d (.f64 c c)) (-.f64 (.f64 c b) (*.f64 a d))))
	39.1b	(/.f64 b c)
	18.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	42.0b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	31.3b	(-.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 d 3) c)) a (*.f64 (/.f64 b d) (-.f64 (/.f64 c d) (pow.f64 (/.f64 c d) 3)))) (/.f64 a d))
▶	17.5b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))

Compiler

Compiled 3118 to 680 computations (78.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	16.5b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series236.0ms (3.5%)

Counts

4 → 132

Calls

4 calls:

108.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
99.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
20.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 139

Calls

4 calls:

11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
4.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify137.0ms (2%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
537×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`
181×	`sub-neg_binary64`

Counts

271 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6415
1	744	5877
2	2552	5818
3	5061	5818

prune200.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	266	5	271
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	271	10	281

Error

1.2b

Counts

281 → 10

Alt Table

Status	Error	Program
	42.0b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
▶	17.4b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	26.2b	(/.f64 1 (/.f64 (fma.f64 d d (.f64 c c)) (-.f64 (.f64 c b) (*.f64 a d))))
	39.1b	(/.f64 b c)
	42.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))))
	35.4b	(neg.f64 (/.f64 a d))
	44.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	20.9b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))
	31.3b	(-.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 d 3) c)) a (*.f64 (/.f64 b d) (-.f64 (/.f64 c d) (pow.f64 (/.f64 c d) 3)))) (/.f64 a d))
	17.6b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))

Compiler

Compiled 7491 to 2252 computations (69.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.1b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	16.5b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series127.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

115.0ms	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
12.0ms	(hypot.f64 d c)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

2 → 83

Calls

2 calls:

6.0ms	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
0.0ms	(hypot.f64 d c)

simplify131.0ms (2%)

Algorithm

1×	egg-herbie

Rules

694×	`times-frac_binary64`
567×	`associate-/l*_binary64`
475×	`associate-/l/_binary64`
441×	`fma-neg_binary64`
291×	`div-sub_binary64`

Counts

155 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	230	4858
1	569	4613
2	1490	4399
3	4548	4352
4	5467	4352

prune195.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	304	10	314

Error

1.2b

Counts

314 → 10

Alt Table

Status	Error	Program
	42.0b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
✓	17.4b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	26.2b	(/.f64 1 (/.f64 (fma.f64 d d (.f64 c c)) (-.f64 (.f64 c b) (*.f64 a d))))
	39.1b	(/.f64 b c)
	42.3b	(/.f64 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)))) (hypot.f64 d c))
▶	17.6b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	35.4b	(neg.f64 (/.f64 a d))
	44.7b	(/.f64 (neg.f64 a) (hypot.f64 d c))
	20.9b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))
	31.3b	(-.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 d 3) c)) a (*.f64 (/.f64 b d) (-.f64 (/.f64 c d) (pow.f64 (/.f64 c d) 3)))) (/.f64 a d))

Compiler

Compiled 8182 to 2003 computations (75.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	16.5b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series349.0ms (5.2%)

Counts

2 → 80

Calls

2 calls:

237.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))

112.0ms

(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))

rewrite105.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

341×	`times-frac_binary64`
251×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
161×	`add-cube-cbrt_binary64`
110×	`sqrt-prod_binary64`

Counts

2 → 276

Calls

2 calls:

39.0ms

(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))

7.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))

simplify325.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
310×	`associate-/l*_binary64`
292×	`associate-*l/_binary64`
274×	`associate-/l/_binary64`
270×	`associate-*r/_binary64`

Counts

356 → 428

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	380	15206
1	1056	13331
2	3405	13258
3	4652	13257
4	5113	13257

prune319.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	522	0	522
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	522	10	532

Error

1.2b

Counts

532 → 10

Alt Table

Status	Error	Program
	42.0b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
✓	17.4b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	26.2b	(/.f64 1 (/.f64 (fma.f64 d d (.f64 c c)) (-.f64 (.f64 c b) (*.f64 a d))))
	39.1b	(/.f64 b c)
	42.3b	(/.f64 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)))) (hypot.f64 d c))
✓	17.6b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	35.4b	(neg.f64 (/.f64 a d))
	44.7b	(/.f64 (neg.f64 a) (hypot.f64 d c))
	20.9b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))
	31.3b	(-.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 d 3) c)) a (*.f64 (/.f64 b d) (-.f64 (/.f64 c d) (pow.f64 (/.f64 c d) 3)))) (/.f64 a d))

Compiler

Compiled 19854 to 3961 computations (80% saved)

regimes1.8s (27.3%)

Accuracy

Total 10.0b remaining (90.4%)

Threshold costs 0b (0%)

Counts

160 → 3

Compiler

Compiled 18096 to 10174 computations (43.8% saved)

bsearch37.0ms (0.6%)

Steps

Iters	Range		Point
7	7.701988703942152e+111	1.3399370062922863e+113	1.2030428421309446e+113
6	-7.996387323058804e+159	-1.5169987728952464e+159	-1.6659650814561475e+159

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	74
1	45	74
2	62	74
3	72	74
4	78	74
5	79	74
6	79	74

end122.0ms (1.8%)

Compiler: Compiled 301 to 171 computations (43.2% saved)

Details

analyze826.0ms (12.4%)

sample1.3s (19.5%)

simplify65.0ms (1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series103.0ms (1.5%)

rewrite12.0ms (0.2%)

simplify93.0ms (1.4%)

prune78.0ms (1.2%)

localize10.0ms (0.1%)

series236.0ms (3.5%)

rewrite32.0ms (0.5%)

simplify137.0ms (2%)

prune200.0ms (3%)

localize8.0ms (0.1%)

series127.0ms (1.9%)

rewrite19.0ms (0.3%)

simplify131.0ms (2%)

prune195.0ms (2.9%)

localize12.0ms (0.2%)

series349.0ms (5.2%)

rewrite105.0ms (1.6%)

simplify325.0ms (4.9%)

prune319.0ms (4.8%)

regimes1.8s (27.3%)

bsearch37.0ms (0.6%)

simplify4.0ms (0.1%)

end122.0ms (1.8%)

Profiling