Details

analyze726.0ms (12%)

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 (18.1%)

Results

1.0s	8256×	body	128	valid
64.0ms	498×	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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

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

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 70 to 36 computations (48.6% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (.f64 a c) (.f64 b d))
✓	26.2b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series108.0ms (1.8%)

Counts

2 → 96

Calls

2 calls:

100.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(+.f64 (.f64 a c) (.f64 b d))

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`fma-def_binary64`
244×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	264	25
2	3782	25

Stop Event

1×	node limit

Counts

2 → 94

Calls

2 calls:

54.0ms	(+.f64 (.f64 a c) (.f64 b d))
54.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-*l/_binary64`
518×	`fma-def_binary64`
407×	`associate-/r/_binary64`
354×	`fma-neg_binary64`
278×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1626
1	114	1542
2	356	1458
3	1797	1410

Stop Event

1×	node limit

Counts

190 → 118

prune96.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Error

2.2b

Counts

119 → 8

Alt Table

Status	Error	Program
	35.7b	(/.f64 a c)
✓	26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
	19.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 a c (.f64 b d))) 2) (hypot.f64 c d)) (/.f64 (cbrt.f64 (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)))
	34.9b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	25.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	38.7b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a c (*.f64 b d))) (hypot.f64 c d)) 2)
▶	19.3b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
	37.2b	(/.f64 b d)

Compiler

Compiled 2539 to 818 computations (67.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a c (*.f64 b d))
✓	0.0b	(hypot.f64 c d)
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
✓	17.9b	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))

series190.0ms (3.1%)

Counts

4 → 168

Calls

4 calls:

92.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
80.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))
9.0ms	(fma.f64 a c (*.f64 b d))
9.0ms	(hypot.f64 c d)

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
254×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
200×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	246	43
2	3155	43

Stop Event

1×	node limit

Counts

4 → 153

Calls

4 calls:

57.0ms	(fma.f64 a c (*.f64 b d))
57.0ms	(hypot.f64 c d)
57.0ms	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (fma.f64 a c (.f64 b d)) (hypot.f64 c d)))
57.0ms	(/.f64 (fma.f64 a c (*.f64 b d)) (hypot.f64 c d))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

560×	`times-frac_binary64`
423×	`associate-/l*_binary64`
332×	`fma-def_binary64`
297×	`cancel-sign-sub-inv_binary64`
277×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	3196
1	373	3046
2	1284	2876

Stop Event

1×	node limit

Counts

321 → 243

prune207.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	294	6	300
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	300	8	308

Error

0.1b

Counts

308 → 8

Alt Table

Status	Error	Program
	25.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 d c) b a))
	44.7b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 c d) a b))
▶	19.3b	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
	31.1b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	32.4b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))

Compiler

Compiled 6884 to 2551 computations (62.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a c (*.f64 b d))
	0.0b	(hypot.f64 c d)
✓	0.3b	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
✓	17.9b	(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

series138.0ms (2.3%)

Counts

2 → 96

Calls

2 calls:

87.0ms	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
51.0ms	(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

281×	`prod-diff_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
207×	`log-pow_binary64`
127×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	252	31
2	3382	31

Stop Event

1×	node limit

Counts

2 → 79

Calls

2 calls:

51.0ms	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
51.0ms	(/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d)))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
567×	`cancel-sign-sub-inv_binary64`
236×	`fma-neg_binary64`
227×	`times-frac_binary64`
209×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	3858
1	491	3302
2	2383	3044

Stop Event

1×	node limit

Counts

175 → 145

prune181.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	292	8	300

Error

0.0b

Counts

300 → 8

Alt Table

Status	Error	Program
	50.9b	(/.f64 (/.f64 1 (hypot.f64 c d)) (+.f64 (.f64 (.f64 (/.f64 d c) (/.f64 d c)) (+.f64 (/.f64 (.f64 b b) (pow.f64 a 3)) (/.f64 1/2 a))) (-.f64 (/.f64 1 a) (.f64 (/.f64 d c) (/.f64 b (*.f64 a a))))))
▶	25.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	44.7b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 c d) a b))
✓	19.3b	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
	31.1b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	32.4b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))

Compiler

Compiled 7710 to 3268 computations (57.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
✓	8.4b	(/.f64 c (/.f64 (fma.f64 d d (*.f64 c c)) a))
✓	9.2b	(/.f64 (fma.f64 d d (*.f64 c c)) a)
✓	18.5b	(/.f64 d (fma.f64 d d (*.f64 c c)))

series209.0ms (3.4%)

Counts

4 → 144

Calls

4 calls:

111.0ms	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
64.0ms	(/.f64 c (/.f64 (fma.f64 d d (*.f64 c c)) a))
21.0ms	(/.f64 (fma.f64 d d (*.f64 c c)) a)
13.0ms	(/.f64 d (fma.f64 d d (*.f64 c c)))

rewrite63.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

463×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
132×	`egg-rr`
122×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	236	59
2	3335	59

Stop Event

1×	node limit

Counts

4 → 132

Calls

4 calls:

60.0ms	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
60.0ms	(/.f64 c (/.f64 (fma.f64 d d (*.f64 c c)) a))
60.0ms	(/.f64 (fma.f64 d d (*.f64 c c)) a)
60.0ms	(/.f64 d (fma.f64 d d (*.f64 c c)))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

388×	`distribute-neg-frac_binary64`
387×	`times-frac_binary64`
309×	`associate-/l*_binary64`
243×	`associate-/r*_binary64`
238×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	3240
1	241	3108
2	751	2964
3	3999	2964

Stop Event

1×	node limit

Counts

276 → 189

prune128.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	189	8	197

Error

0.0b

Counts

197 → 8

Alt Table

Status	Error	Program
	50.9b	(/.f64 (/.f64 1 (hypot.f64 c d)) (+.f64 (.f64 (.f64 (/.f64 d c) (/.f64 d c)) (+.f64 (/.f64 (.f64 b b) (pow.f64 a 3)) (/.f64 1/2 a))) (-.f64 (/.f64 1 a) (.f64 (/.f64 d c) (/.f64 b (*.f64 a a))))))
✓	25.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 c (/.f64 (fma.f64 d d (.f64 c c)) a)))
	44.7b	(*.f64 (/.f64 1 (hypot.f64 c d)) (fma.f64 (/.f64 c d) a b))
✓	19.3b	(/.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (hypot.f64 c d) (fma.f64 a c (*.f64 b d))))
	31.1b	(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
	32.4b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 c d)) (neg.f64 (fma.f64 (/.f64 d c) b a)))

Compiler

Compiled 4810 to 1849 computations (61.6% saved)

regimes2.3s (37.2%)

Accuracy

Total 11.2b remaining (98.6%)

Threshold costs 0b (0%)

Counts

121 → 5

Compiler

Compiled 11198 to 6849 computations (38.8% saved)

bsearch83.0ms (1.4%)

Steps

Iters	Range		Point
9	3.363924642192831e+135	3.5965325781940086e+140	1.2722428837589733e+140
9	2.634451215286903e-71	3.60595376629138e-65	2.670610561569208e-71
8	-2.4141280899525958e-105	-1.8387138583883085e-108	-3.283521020638581e-106
7	-9.881632775610893e+154	-1.2999618955171796e+153	-1.1870115366769325e+154

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	113
1	42	113

Stop Event

1×

saturated

end132.0ms (2.2%)

Compiler: Compiled 333 to 170 computations (48.9% saved)

Details

analyze726.0ms (12%)

sample1.1s (18.1%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.2%)

series108.0ms (1.8%)

rewrite56.0ms (0.9%)

simplify42.0ms (0.7%)

prune96.0ms (1.6%)

localize9.0ms (0.2%)

series190.0ms (3.1%)

rewrite60.0ms (1%)

simplify55.0ms (0.9%)

prune207.0ms (3.4%)

localize9.0ms (0.2%)

series138.0ms (2.3%)

rewrite53.0ms (0.9%)

simplify62.0ms (1%)

prune181.0ms (3%)

localize10.0ms (0.2%)

series209.0ms (3.4%)

rewrite63.0ms (1%)

simplify73.0ms (1.2%)

prune128.0ms (2.1%)

regimes2.3s (37.2%)

bsearch83.0ms (1.4%)

simplify4.0ms (0.1%)

end132.0ms (2.2%)

Profiling