Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample648.0ms (28.3%)

Results

636.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% saved)

preprocess18.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(hypot.f64 x x)

series4.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(hypot.f64 x x)	x	-inf
1.0ms	(hypot.f64 x x)	x	inf
1.0ms	(hypot.f64 x x)	x	0

rewrite27.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
227×	`add-cube-cbrt_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	700	4

Stop Event

1×	node limit

Counts

1 → 40

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

52 → 43

prune21.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Error

0.0b

Counts

44 → 7

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
✓	0.2b	(hypot.f64 x x)
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	32.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	31.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	31.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 481 to 233 computations (51.6% saved)

localize18.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.2b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series18.0ms (0.8%)

Counts

2 → 0

Calls

6 calls:

4.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)	x	0
4.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)	x	-inf
4.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)	x	inf
2.0ms	(sqrt.f64 (hypot.f64 x x))	x	0
2.0ms	(sqrt.f64 (hypot.f64 x x))	x	-inf

rewrite37.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
339×	`pow1_binary64`
263×	`unpow-prod-down_binary64`
191×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	124	10
2	1142	10

Stop Event

1×	node limit

Counts

2 → 88

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

88 → 88

prune54.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Error

0.0b

Counts

138 → 7

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓	0.2b	(hypot.f64 x x)
	32.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	31.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	31.4b	(*.f64 (sqrt.f64 2) x)
▶	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

Compiler

Compiled 1561 to 826 computations (47.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.2b	(hypot.f64 x x)
✓	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

series399.0ms (17.4%)

Counts

3 → 36

Calls

9 calls:

101.0ms	(pow.f64 (hypot.f64 x x) 1/4)	x	0
61.0ms	(pow.f64 (hypot.f64 x x) 3/4)	x	0
60.0ms	(pow.f64 (hypot.f64 x x) 1/4)	x	-inf
58.0ms	(pow.f64 (hypot.f64 x x) 3/4)	x	inf
58.0ms	(pow.f64 (hypot.f64 x x) 3/4)	x	-inf

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	162	18
2	1753	18

Stop Event

1×	node limit

Counts

3 → 64

simplify31.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-l_binary64`
374×	`associate-r_binary64`
322×	`fma-def_binary64`
240×	`unswap-sqr_binary64`
177×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	464
1	74	464
2	156	416
3	331	320
4	821	312
5	1983	312

Stop Event

1×	node limit

Counts

100 → 77

prune91.0ms (4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	160	10	170

Error

0.0b

Counts

170 → 10

Alt Table

Status	Error	Program
	1.9b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x))) 3/4))
✓	0.2b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	1.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (hypot.f64 x x) 3/4))
	32.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	31.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	31.4b	(*.f64 (sqrt.f64 2) x)
▶	0.5b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8)))
✓	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

Compiler

Compiled 2716 to 1414 computations (47.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 3/8)
	0.2b	(hypot.f64 x x)
✓	0.3b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8)))
✓	0.4b	(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))

series464.0ms (20.2%)

Counts

3 → 36

Calls

9 calls:

101.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))	x	0
90.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))	x	-inf
88.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 3/8) (pow.f64 (hypot.f64 x x) 3/8))	x	inf
64.0ms	(pow.f64 (hypot.f64 x x) 3/8)	x	inf
59.0ms	(pow.f64 (hypot.f64 x x) 3/8)	x	0

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
138×	`log1p-udef_binary64`
87×	`add-log-exp_binary64`
86×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	200	18
2	2196	18

Stop Event

1×	node limit

Counts

3 → 54

simplify34.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
282×	`distribute-rgt-in_binary64`
281×	`exp-sum_binary64`
221×	`distribute-lft-in_binary64`
159×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	520
1	106	500
2	240	440
3	615	356
4	1991	312

Stop Event

1×	node limit

Counts

90 → 68

prune126.0ms (5.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	5	6
Picked	1	0	1
Done	0	3	3
Total	222	9	231

Error

0.0b

Counts

231 → 9

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
✓	0.2b	(hypot.f64 x x)
	1.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 1/4)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (hypot.f64 x x) 3/4))
	32.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	31.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	31.4b	(*.f64 (sqrt.f64 2) x)
	6.8b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.f64 (pow.f64 (hypot.f64 x x) 3/8) (cbrt.f64 (pow.f64 (hypot.f64 x x) 9/8))))
✓	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

Compiler

Compiled 4537 to 2340 computations (48.4% saved)

regimes73.0ms (3.2%)

Accuracy

Total 0.1b remaining (89.2%)

Threshold costs 0.1b (89.2%)

Counts

20 → 1

Compiler

Compiled 914 to 568 computations (37.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×

saturated

end95.0ms (4.2%)

Stop Event

1×

fuel

Compiler

Compiled 101 to 61 computations (39.6% saved)

Details

analyze4.0ms (0.2%)

sample648.0ms (28.3%)

preprocess18.0ms (0.8%)

simplify6.0ms (0.3%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.2%)

rewrite27.0ms (1.2%)

simplify12.0ms (0.5%)

prune21.0ms (0.9%)

localize18.0ms (0.8%)

series18.0ms (0.8%)

rewrite37.0ms (1.6%)

simplify7.0ms (0.3%)

prune54.0ms (2.4%)

localize10.0ms (0.4%)

series399.0ms (17.4%)

rewrite40.0ms (1.7%)

simplify31.0ms (1.4%)

prune91.0ms (4%)

localize9.0ms (0.4%)

series464.0ms (20.2%)

rewrite40.0ms (1.7%)

simplify34.0ms (1.5%)

prune126.0ms (5.5%)

regimes73.0ms (3.2%)

simplify3.0ms (0.1%)

end95.0ms (4.2%)

Profiling