Details

analyze17.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.1s (45.6%)

Results

992.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify107.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

32.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.8b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	32.1b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series22.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
8.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

rewrite61.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

560×	`log-prod_binary64`
377×	`prod-diff_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
186×	`log-pow_binary64`

Counts

2 → 67

Calls

2 calls:

59.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
59.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	246	34
2	2736	34
3	5359	34
0	0	0
1	0	0

simplify79.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-neg_binary64`
502×	`associate-*l/_binary64`
472×	`associate-*r/_binary64`
368×	`fma-def_binary64`
322×	`associate-/r/_binary64`

Counts

115 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	807
1	121	753
2	326	741
3	1272	723
4	4300	669
5	4942	669
6	4998	669
7	4958	669

prune53.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Error

0.1b

Counts

88 → 3

Alt Table

Status	Error	Program
	32.8b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))))
▶	28.5b	-1
	34.7b	1

Compiler

Compiled 2014 to 1141 computations (43.3% saved)

localize0.0ms (0%)

prune5.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.1b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	32.8b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))))
✓	28.5b	-1
	34.7b	1

Compiler

Compiled 91 to 63 computations (30.8% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))
✓	0.0b	(log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))))
	3.1b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	32.1b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2))

series112.0ms (4.5%)

Counts

3 → 72

Calls

3 calls:

60.0ms

(log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))))

30.0ms

(exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))

22.0ms

(/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2))

rewrite102.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

323×	`prod-diff_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
233×	`log-pow_binary64`
158×	`fma-def_binary64`

Counts

3 → 99

Calls

3 calls:

99.0ms

(exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))

99.0ms

(log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2)))))

99.0ms

(/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 y 2)) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	299	74
2	3183	74
3	4981	74
4	5113	74
0	0	0
1	0	0

simplify87.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

681×	`times-frac_binary64`
547×	`fma-def_binary64`
444×	`fma-neg_binary64`
435×	`associate-/r*_binary64`
397×	`associate-/l*_binary64`

Counts

171 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2736
1	412	2139
2	1386	2004
3	4440	2004
4	4921	2004

prune374.0ms (14.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	358	0	358
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	358	3	361

Error

0.1b

Counts

361 → 3

Alt Table

Status	Error	Program
✓	32.8b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))))
✓	28.5b	-1
▶	34.7b	1

Compiler

Compiled 16948 to 10639 computations (37.2% saved)

localize0.0ms (0%)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

0.1b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	32.8b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (pow.f64 (hypot.f64 x (.f64 y 2)) 2))))))
✓	28.5b	-1
✓	34.7b	1

Compiler

Compiled 47 to 33 computations (29.8% saved)

regimes161.0ms (6.4%)

Accuracy

Total 15.1b remaining (98%)

Threshold costs 0b (0%)

Counts

8 → 5

Compiler

Compiled 1030 to 682 computations (33.8% saved)

bsearch59.0ms (2.4%)

Steps

Iters	Range		Point
7	1.028498402671336e+132	9.691593578798375e+133	1.1936372032097385e+132
8	1.4987034732775623e+82	7.662732224284799e+86	5.032080348772434e+85
8	9.882687188899827e-60	5.521665993345349e-57	5.608377203181558e-58
3	-2.765959451628873e+27	-1.817321150964782e+25	-4.3416912027427956e+26

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	34	88
2	33	88

end87.0ms (3.5%)

Compiler: Compiled 169 to 119 computations (29.6% saved)

Details

analyze17.0ms (0.7%)

sample1.1s (45.6%)

simplify107.0ms (4.2%)

prune5.0ms (0.2%)

localize11.0ms (0.4%)

series22.0ms (0.9%)

rewrite61.0ms (2.4%)

simplify79.0ms (3.1%)

prune53.0ms (2.1%)

localize0.0ms (0%)

prune5.0ms (0.2%)

localize14.0ms (0.6%)

series112.0ms (4.5%)

rewrite102.0ms (4.1%)

simplify87.0ms (3.5%)

prune374.0ms (14.9%)

localize0.0ms (0%)

prune3.0ms (0.1%)

regimes161.0ms (6.4%)

bsearch59.0ms (2.4%)

simplify4.0ms (0.1%)

end87.0ms (3.5%)

Profiling