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
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample783.0ms (45.7%)

Results

593.0ms	7471×	body	128	valid
116.0ms	445×	body	1024	valid
46.0ms	232×	body	512	valid
14.0ms	108×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess38.0ms (2.2%)

Algorithm

2×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
87×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	43	10
3	101	8
4	229	8
5	361	8
6	545	8
7	816	8
8	1369	8
9	1522	8
10	1835	8
11	2255	8
12	2364	8
13	2368	8
14	2368	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 8 computations (20% saved)

simplify30.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
87×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	43	10
3	101	8
4	229	8
5	361	8
6	545	8
7	816	8
8	1369	8
9	1522	8
10	1835	8
11	2255	8
12	2364	8
13	2368	8
14	2368	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (fma.f64 x -9 6))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

Compiler

Compiled 50 to 38 computations (24% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -9 6)
✓	0.1b	(*.f64 x (fma.f64 x -9 6))

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(*.f64 x (fma.f64 x -9 6))	x	-inf
1.0ms	(*.f64 x (fma.f64 x -9 6))	x	inf
1.0ms	(*.f64 x (fma.f64 x -9 6))	x	0
0.0ms	(fma.f64 x -9 6)	x	-inf
0.0ms	(fma.f64 x -9 6)	x	inf

rewrite35.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`log1p-expm1-u_binary64`
506×	`expm1-log1p-u_binary64`
285×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`
147×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1346	13

Stop Event

1×	node limit

Counts

2 → 54

simplify36.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-neg_binary64`
474×	`fma-def_binary64`
450×	`cancel-sign-sub-inv_binary64`
315×	`associate-l_binary64`
255×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	32	189
2	61	144
3	132	144
4	424	144
5	1493	144
6	2879	144
7	4277	144

Stop Event

1×	node limit

Counts

78 → 64

prune46.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Error

0.1b

Counts

66 → 8

Alt Table

Status	Error	Program
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
	2.6b	(.f64 x (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -9 6))) 2) 3) (cbrt.f64 (fma.f64 x -9 6))))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	1.4b	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -9 6)) (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 2)))
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	43.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	10.3b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))

Compiler

Compiled 845 to 663 computations (21.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series10.0ms (0.6%)

Counts

2 → 3

Calls

6 calls:

5.0ms	(*.f64 9 (pow.f64 x 2))	x	0
1.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))	x	-inf
1.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))	x	inf
1.0ms	(*.f64 9 (pow.f64 x 2))	x	inf
1.0ms	(*.f64 9 (pow.f64 x 2))	x	-inf

rewrite49.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`
92×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	208	18
2	2480	18

Stop Event

1×	node limit

Counts

2 → 63

simplify61.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

624×	`sqr-pow_binary64`
513×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
279×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	26	18
3	51	18
4	124	18
5	367	18
6	1383	18
7	2272	18
8	2436	18
9	2649	18
10	2869	18
11	3169	18
12	3569	18
13	4057	18
14	4618	18

Stop Event

1×	node limit

Counts

66 → 66

prune56.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	66	8	74

Error

0.0b

Counts

74 → 8

Alt Table

Status	Error	Program
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
▶	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	2.6b	(.f64 x (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -9 6))) 2) 3) (cbrt.f64 (fma.f64 x -9 6))))
	0.2b	(+.f64 (fma.f64 x 6 (.f64 (.f64 x x) -9)) (+.f64 (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x))) (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x)))))
	0.3b	(-.f64 (.f64 6 x) (pow.f64 (.f64 x 3) 2))
	43.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	10.3b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))

Compiler

Compiled 1418 to 854 computations (39.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
✓	0.2b	(.f64 (.f64 x x) -9)

series5.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))	x	-inf
1.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))	x	inf
1.0ms	(.f64 (.f64 x x) -9)	x	0
1.0ms	(.f64 (.f64 x x) -9)	x	-inf
1.0ms	(.f64 (.f64 x x) -9)	x	inf

rewrite37.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log1p-expm1-u_binary64`
577×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
123×	`prod-diff_binary64`
120×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	144	17
2	1597	17

Stop Event

1×	node limit

Counts

2 → 46

simplify36.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
596×	`fma-def_binary64`
293×	`distribute-rgt-neg-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
251×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	219
1	24	201
2	50	192
3	134	174
4	402	174
5	1345	174
6	2596	174
7	4165	174

Stop Event

1×	node limit

Counts

70 → 52

prune37.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	52	8	60

Error

0.0b

Counts

60 → 8

Alt Table

Status	Error	Program
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
✓	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	2.6b	(.f64 x (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -9 6))) 2) 3) (cbrt.f64 (fma.f64 x -9 6))))
▶	0.2b	(+.f64 (fma.f64 x 6 (.f64 (.f64 x x) -9)) (+.f64 (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x))) (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x)))))
	43.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	10.3b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	0.2b	(*.f64 x (fma.f64 -9 x 6))

Compiler

Compiled 839 to 614 computations (26.8% saved)

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	0.2b	(.f64 (.f64 x x) -9)
✓	0.2b	(.f64 9 (.f64 x x))
✓	34.6b	(fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (*.f64 x x)))

series6.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (*.f64 x x)))	x	-inf
1.0ms	(fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (*.f64 x x)))	x	inf
1.0ms	(fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (*.f64 x x)))	x	0
1.0ms	(.f64 9 (.f64 x x))	x	-inf
1.0ms	(.f64 9 (.f64 x x))	x	inf

rewrite37.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`prod-diff_binary64`
534×	`log1p-expm1-u_binary64`
534×	`expm1-log1p-u_binary64`
108×	`expm1-udef_binary64`
108×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	23
1	150	20
2	1825	20

Stop Event

1×	node limit

Counts

2 → 36

simplify59.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
274×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	13	96
2	23	96
3	44	96
4	105	96
5	320	96
6	1203	96
7	2081	96
8	2245	96
9	2428	96
10	2636	96
11	2925	96
12	3318	96
13	3798	96
14	4359	96

Stop Event

1×	node limit

Counts

60 → 39

prune122.0ms (7.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	130	8	138

Error

0.0b

Counts

138 → 8

Alt Table

Status	Error	Program
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
✓	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	2.6b	(.f64 x (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -9 6))) 2) 3) (cbrt.f64 (fma.f64 x -9 6))))
✓	0.2b	(+.f64 (fma.f64 x 6 (.f64 (.f64 x x) -9)) (+.f64 (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x))) (fma.f64 (neg.f64 (.f64 x x)) 9 (.f64 9 (.f64 x x)))))
	43.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	10.3b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	0.2b	(*.f64 x (fma.f64 -9 x 6))

Compiler

Compiled 4688 to 2376 computations (49.3% saved)

regimes76.0ms (4.4%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Counts

39 → 1

Compiler

Compiled 986 to 706 computations (28.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

end113.0ms (6.6%)

Stop Event

1×

fuel

Compiler

Compiled 126 to 88 computations (30.2% saved)

Details

analyze4.0ms (0.2%)

sample783.0ms (45.7%)

preprocess38.0ms (2.2%)

simplify30.0ms (1.7%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series4.0ms (0.2%)

rewrite35.0ms (2.1%)

simplify36.0ms (2.1%)

prune46.0ms (2.7%)

localize5.0ms (0.3%)

series10.0ms (0.6%)

rewrite49.0ms (2.9%)

simplify61.0ms (3.6%)

prune56.0ms (3.3%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite37.0ms (2.2%)

simplify36.0ms (2.1%)

prune37.0ms (2.2%)

localize11.0ms (0.7%)

series6.0ms (0.4%)

rewrite37.0ms (2.1%)

simplify59.0ms (3.5%)

prune122.0ms (7.1%)

regimes76.0ms (4.4%)

simplify2.0ms (0.1%)

end113.0ms (6.6%)

Profiling