Details

analyze673.0ms (8.1%)

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
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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

prune3.0ms (0%)

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

Error

27.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.3b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
26.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

27.2b

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 → 47

Calls

2 calls:

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

Compiler

Compiled 1272 to 170 computations (86.6% saved)

series88.0ms (1.1%)

Error

4.6b

Counts

2 → 48

Calls

2 calls:

53.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
25.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1446 to 906 computations (37.3% saved)

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-l_binary64`
380×	`fma-neg_binary64`
334×	`fma-def_binary64`
331×	`associate-r_binary64`
281×	`unswap-sqr_binary64`

Counts

95 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1918
1	287	1811
2	875	1787
3	2820	1787
4	4668	1787
5	5175	1787

prune34.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Error

0.1b

Counts

84 → 6

Alt Table

Status	Error	Program
	39.3b	(.f64 (/.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	28.3b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	35.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	26.4b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	27.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 d d (.f64 c c))) (cbrt.f64 (fma.f64 d d (.f64 c c))))) (/.f64 (fma.f64 d b (.f64 c a)) (cbrt.f64 (fma.f64 d d (.f64 c c)))))

Compiler

Compiled 1246 to 285 computations (77.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (hypot.f64 d c))
0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
0.3b	(fma.f64 d b (*.f64 c a))
16.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite101.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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 → 130

Calls

4 calls:

9.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
2.0ms	(/.f64 1 (hypot.f64 d c))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

Compiler

Compiled 3240 to 798 computations (75.4% saved)

series232.0ms (2.8%)

Error

0.1b

Counts

4 → 92

Calls

4 calls:

82.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
68.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
30.0ms	(fma.f64 d b (*.f64 c a))
28.0ms	(/.f64 1 (hypot.f64 d c))

Compiler

Compiled 3684 to 2368 computations (35.7% saved)

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

615×	`times-frac_binary64`
455×	`fma-def_binary64`
449×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
208×	`associate-r_binary64`

Counts

222 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	5001
1	587	4454
2	2099	4369
3	5016	4369

prune63.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	165	9	174

Error

0.0b

Counts

174 → 9

Alt Table

Status	Error	Program
	18.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))) (hypot.f64 d c)) (cbrt.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
	26.4b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	18.1b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	44.0b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	46.7b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))
	18.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (/.f64 1 (hypot.f64 d c)))))
	35.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	24.5b	(/.f64 (*.f64 (/.f64 a (hypot.f64 d c)) c) (hypot.f64 d c))
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 2125 to 539 computations (74.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(fma.f64 d b (*.f64 c a))
0.3b	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
16.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite218.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

350×	`times-frac_binary64`
261×	`add-sqr-sqrt_binary64`
181×	`*-un-lft-identity_binary64`
171×	`add-cube-cbrt_binary64`
110×	`sqrt-prod_binary64`

Counts

4 → 314

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
6.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

Compiler

Compiled 10311 to 1796 computations (82.6% saved)

series299.0ms (3.6%)

Error

0.0b

Counts

4 → 100

Calls

4 calls:

104.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
77.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
65.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
32.0ms	(fma.f64 d b (*.f64 c a))

Compiler

Compiled 4878 to 3090 computations (36.7% saved)

simplify301.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

461×	`associate-*l/_binary64`
392×	`fma-def_binary64`
362×	`associate-*r/_binary64`
362×	`associate-/l*_binary64`
336×	`associate-r_binary64`

Counts

414 → 339

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	15752
1	1191	13652
2	3815	13521
3	5006	13521

prune114.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	336	3	339
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	339	9	348

Error

0.0b

Counts

348 → 9

Alt Table

Status	Error	Program
	46.7b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))
	25.3b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	44.1b	(/.f64 (/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
▶	18.2b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
	35.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	26.4b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	24.5b	(/.f64 (*.f64 (/.f64 a (hypot.f64 d c)) c) (hypot.f64 d c))
	44.0b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 5932 to 1216 computations (79.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))
0.3b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
0.4b	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))
16.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite784.0ms (9.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1485×	`times-frac_binary64`
1125×	`add-sqr-sqrt_binary64`
1062×	`sqrt-prod_binary64`
652×	`*-un-lft-identity_binary64`
610×	`add-cube-cbrt_binary64`

Counts

4 → 914

Calls

4 calls:

216.0ms	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
10.0ms	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))
7.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

Compiler

Compiled 29099 to 5783 computations (80.1% saved)

series367.0ms (4.4%)

Error

0.0b

Counts

4 → 87

Calls

4 calls:

172.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))
81.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
68.0ms	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
20.0ms	(/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c))))

Compiler

Compiled 5479 to 3388 computations (38.2% saved)

simplify895.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

472×	`associate-/l*_binary64`
443×	`fma-def_binary64`
405×	`associate-/l/_binary64`
399×	`associate-r_binary64`
398×	`associate-l_binary64`

Counts

1001 → 802

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	614	50230
1	1792	45361
2	4778	45305
3	5132	45305

prune246.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	801	1	802
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	802	9	811

Error

0.0b

Counts

811 → 9

Alt Table

Status	Error	Program
	46.7b	(/.f64 (fma.f64 (/.f64 c d) a b) (hypot.f64 d c))
	44.1b	(/.f64 (/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	18.2b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
	35.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	26.4b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	18.0b	(.f64 (pow.f64 (hypot.f64 d c) -3/4) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (sqrt.f64 (hypot.f64 d c)))))
	24.5b	(/.f64 (*.f64 (/.f64 a (hypot.f64 d c)) c) (hypot.f64 d c))
	44.0b	(/.f64 (neg.f64 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
✓	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 14941 to 3114 computations (79.2% saved)

regimes2.6s (31.3%)

Accuracy

Total 10.0b remaining (94.3%)

Threshold costs 0b (0%)

Compiler

Compiled 24274 to 12331 computations (49.2% saved)

bsearch87.0ms (1%)

Steps

Iters	Range		Point
9	2475315022.3094993	207132584154538.22	204889703146200.6
7	2.9932232504542783e-189	3.6764713138205014e-187	4.578520467817402e-188
9	-9.84002776956972e-160	-1.2284656606392705e-164	-7.366462231695976e-163
11	-2.8625432284889564e+94	-1.8983070660487937e+73	-1.9291899314496838e+93

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	108
1	40	108
2	39	108

end1.0ms (0%)

Compiler: Compiled 79 to 31 computations (60.8% saved)

sample869.0ms (10.4%)

Algorithm

1×

intervals

Results

424.0ms	8000×	body	128	valid
26.0ms	482×	body	128	invalid

Compiler

Compiled 285 to 141 computations (50.5% saved)

Details

analyze673.0ms (8.1%)

sample27.0ms (0.3%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite59.0ms (0.7%)

series88.0ms (1.1%)

simplify102.0ms (1.2%)

prune34.0ms (0.4%)

localize10.0ms (0.1%)

rewrite101.0ms (1.2%)

series232.0ms (2.8%)

simplify119.0ms (1.4%)

prune63.0ms (0.8%)

localize13.0ms (0.2%)

rewrite218.0ms (2.6%)

series299.0ms (3.6%)

simplify301.0ms (3.6%)

prune114.0ms (1.4%)

localize16.0ms (0.2%)

rewrite784.0ms (9.4%)

series367.0ms (4.4%)

simplify895.0ms (10.7%)

prune246.0ms (2.9%)

regimes2.6s (31.3%)

bsearch87.0ms (1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample869.0ms (10.4%)

Profiling