Details

analyze694.0ms (8%)

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)

sample1.1s (12.5%)

Results

995.0ms	8256×	body	128	valid
58.0ms	471×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

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

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

25.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	25.9b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
▶	25.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 104 to 54 computations (48.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 c c) (.f64 d d))
✓	0.5b	(+.f64 (.f64 a c) (.f64 b d))
✓	25.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series96.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

81.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(+.f64 (.f64 a c) (.f64 b d))
6.0ms	(+.f64 (.f64 c c) (.f64 d d))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 61

Calls

3 calls:

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

simplify126.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-l_binary64`
491×	`fma-def_binary64`
421×	`associate-r_binary64`
343×	`times-frac_binary64`
328×	`fma-neg_binary64`

Counts

181 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	3026
1	382	2904
2	1251	2820
3	4751	2808
4	4975	2808
5	4968	2808

prune95.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	6	138

Error

0.0b

Counts

138 → 6

Alt Table

Status	Error	Program
	31.3b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
▶	16.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	33.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	17.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	25.8b	(fma.f64 (/.f64 d (fma.f64 d d (.f64 c c))) b (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	25.9b	(/.f64 1 (/.f64 (fma.f64 d d (.f64 c c)) (fma.f64 d b (.f64 c a))))

Compiler

Compiled 3372 to 649 computations (80.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	15.9b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series222.0ms (2.6%)

Counts

4 → 168

Calls

4 calls:

104.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
96.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
12.0ms	(hypot.f64 d c)
9.0ms	(fma.f64 d b (*.f64 c a))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (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))
0.0ms	(hypot.f64 d c)

simplify144.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
425×	`fma-neg_binary64`
389×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
283×	`distribute-rgt-in_binary64`

Counts

275 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	5683
1	623	5331
2	2083	5152
3	4804	5152
4	5030	5152

prune252.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	301	5	306
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	305	7	312

Error

0.0b

Counts

312 → 7

Alt Table

Status	Error	Program
▶	16.8b	(/.f64 (.f64 1 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (hypot.f64 d c))
	31.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	31.3b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	33.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	17.1b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
	43.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
	24.3b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 7918 to 2444 computations (69.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 d c)
	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.1b	(/.f64 (.f64 1 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (hypot.f64 d c))
	15.9b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series138.0ms (1.6%)

Counts

1 → 48

Calls

1 calls:

138.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`div-exp_binary64`
4×	`cbrt-undiv_binary64`
4×	`prod-exp_binary64`

Counts

1 → 28

Calls

1 calls:

5.0ms

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

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
563×	`fma-neg_binary64`
466×	`times-frac_binary64`
352×	`associate-/l*_binary64`
263×	`distribute-rgt-neg-in_binary64`

Counts

76 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	99	2092
1	242	1844
2	783	1742
3	2901	1724
4	4702	1688
5	5106	1688

prune178.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	257	7	264

Error

0.0b

Counts

264 → 7

Alt Table

Status	Error	Program
✓	16.8b	(/.f64 (.f64 1 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (hypot.f64 d c))
	31.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	31.3b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	33.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
▶	17.1b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
	43.1b	(/.f64 (*.f64 1 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	24.3b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 6355 to 2169 computations (65.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
✓	6.5b	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	9.4b	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))

series376.0ms (4.4%)

Counts

4 → 136

Calls

4 calls:

131.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))
121.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
103.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
21.0ms	(sqrt.f64 (hypot.f64 d c))

rewrite143.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

569×	`times-frac_binary64`
367×	`add-sqr-sqrt_binary64`
294×	`*-un-lft-identity_binary64`
287×	`add-cube-cbrt_binary64`
282×	`sqrt-prod_binary64`

Counts

4 → 435

Calls

4 calls:

39.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
11.0ms	(/.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
3.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c)))
1.0ms	(sqrt.f64 (hypot.f64 d c))

simplify517.0ms (6%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
350×	`associate-/l/_binary64`
331×	`associate-/l*_binary64`
313×	`associate-*l/_binary64`
301×	`associate-*r/_binary64`

Counts

571 → 620

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	484	19970
1	1325	18582
2	4045	17818
3	4902	17818
4	4992	17818
5	4960	17818

prune531.0ms (6.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	649	1	650
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	651	6	657

Error

0.0b

Counts

657 → 6

Alt Table

Status	Error	Program
	31.3b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	33.1b	(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
	43.1b	(/.f64 (*.f64 1 (fma.f64 (/.f64 d c) b a)) (hypot.f64 d c))
	17.0b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (.f64 (fma.f64 d b (*.f64 c a)) (/.f64 1 (sqrt.f64 (hypot.f64 d c)))) (sqrt.f64 (hypot.f64 d c))))
	24.3b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
✓	16.8b	(/.f64 (.f64 1 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (hypot.f64 d c))

Compiler

Compiled 24014 to 4853 computations (79.8% saved)

regimes3.7s (42.5%)

Accuracy

Total 9.6b remaining (98.1%)

Threshold costs 0b (0%)

Counts

230 → 5

Compiler

Compiled 24304 to 13932 computations (42.7% saved)

bsearch72.0ms (0.8%)

Steps

Iters	Range		Point
6	7.246757509829897e+167	4.731472614573352e+168	7.346913309450737e+167
6	4.540840466594869e-207	2.893572695982277e-206	2.840945379294546e-206
7	-3.58980974963377e-213	-2.085940664827632e-215	-3.503819725312034e-213
6	-4.203831380111236e+129	-7.79835634961433e+128	-1.258944315537144e+129

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	112
1	60	112
2	76	112
3	83	112
4	88	112
5	90	112
6	88	112

end111.0ms (1.3%)

Compiler: Compiled 278 to 134 computations (51.8% saved)

Details

analyze694.0ms (8%)

sample1.1s (12.5%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series96.0ms (1.1%)

rewrite16.0ms (0.2%)

simplify126.0ms (1.5%)

prune95.0ms (1.1%)

localize9.0ms (0.1%)

series222.0ms (2.6%)

rewrite19.0ms (0.2%)

simplify144.0ms (1.7%)

prune252.0ms (2.9%)

localize9.0ms (0.1%)

series138.0ms (1.6%)

rewrite8.0ms (0.1%)

simplify91.0ms (1.1%)

prune178.0ms (2.1%)

localize11.0ms (0.1%)

series376.0ms (4.4%)

rewrite143.0ms (1.7%)

simplify517.0ms (6%)

prune531.0ms (6.2%)

regimes3.7s (42.5%)

bsearch72.0ms (0.8%)

simplify6.0ms (0.1%)

end111.0ms (1.3%)

Profiling