Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.7s (73%)

Results

847.0ms	2188×	body	2048	valid
385.0ms	4280×	body	128	valid
298.0ms	1034×	body	1024	valid
122.0ms	517×	body	512	valid
37.0ms	237×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series2.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`expm1-log1p-u_binary64`
688×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	2154	11

Stop Event

1×	node limit

Counts

1 → 50

Calls

1 calls:

35.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

50 → 50

prune38.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	2	51

Error

0.0b

Counts

51 → 2

Alt Table

Status	Error	Program
	15.9b	(fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
▶	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 916 to 558 computations (39.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 N (+.f64 N 1))
✓	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
2.0ms	(*.f64 N (+.f64 N 1))

rewrite39.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

817×	`log1p-expm1-u_binary64`
817×	`expm1-log1p-u_binary64`
605×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	218	16
2	2261	16

Stop Event

1×	node limit

Counts

2 → 41

Calls

2 calls:

38.0ms	(*.f64 N (+.f64 N 1))
38.0ms	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify52.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-def_binary64`
466×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
234×	`cube-prod_binary64`
220×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	228
1	20	186
2	35	186
3	54	186
4	112	186
5	291	186
6	976	186
7	2227	186
8	2688	186
9	2904	186
10	3140	186
11	3487	186
12	3924	186
13	4423	186

Stop Event

1×	node limit

Counts

65 → 47

prune38.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

0.0b

Counts

49 → 5

Alt Table

Status	Error	Program
	1.4b	(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
✓	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	0.3b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
	10.2b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
	0.7b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)

Compiler

Compiled 807 to 479 computations (40.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)
✓	12.9b	(cbrt.f64 (fma.f64 N N N))

series13.0ms (0.6%)

Counts

3 → 12

Calls

3 calls:

8.0ms	(pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)
4.0ms	(cbrt.f64 (fma.f64 N N N))
1.0ms	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
508×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	249	23
2	2267	23

Stop Event

1×	node limit

Counts

3 → 69

Calls

3 calls:

39.0ms	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
39.0ms	(pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)
39.0ms	(cbrt.f64 (fma.f64 N N N))

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	132
1	11	132
2	17	132
3	26	132
4	34	132
5	38	132
6	50	132
7	63	132
8	68	132
9	69	132

Stop Event

1×

saturated

Counts

81 → 70

prune51.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Error

0.0b

Counts

75 → 5

Alt Table

Status	Error	Program
	1.4b	(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
✓	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	0.3b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
	10.2b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
▶	0.7b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)

Compiler

Compiled 1335 to 711 computations (46.7% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.7b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓	12.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series11.0ms (0.5%)

Counts

3 → 12

Calls

3 calls:

6.0ms	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
3.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite37.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

683×	`log1p-expm1-u_binary64`
683×	`expm1-log1p-u_binary64`
247×	`prod-diff_binary64`
131×	`log1p-udef_binary64`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	186	35
2	1892	35

Stop Event

1×	node limit

Counts

3 → 65

Calls

3 calls:

36.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
36.0ms	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
36.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	132
1	11	132
2	17	132
3	26	132
4	34	132
5	38	132
6	50	132
7	63	132
8	68	132
9	69	132

Stop Event

1×

saturated

Counts

77 → 47

prune28.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	47	5	52

Error

0.0b

Counts

52 → 5

Alt Table

Status	Error	Program
	1.4b	(*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
✓	0.1b	(atan2.f64 (+.f64 1 (-.f64 N N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
	0.7b	(.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1/4) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
	10.2b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
✓	0.7b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)

Compiler

Compiled 836 to 557 computations (33.4% saved)

regimes97.0ms (4.1%)

Accuracy

Total 0.0b remaining (11.1%)

Threshold costs 0.0b (11.1%)

Counts

60 → 1

Compiler

Compiled 1824 to 1344 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	11	15

Stop Event

1×

saturated

end81.0ms (3.4%)

Compiler: Compiled 114 to 80 computations (29.8% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Details

analyze1.0ms (0%)

sample1.7s (73%)

simplify11.0ms (0.5%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite36.0ms (1.5%)

simplify5.0ms (0.2%)

prune38.0ms (1.6%)

localize6.0ms (0.3%)

series4.0ms (0.2%)

rewrite39.0ms (1.7%)

simplify52.0ms (2.2%)

prune38.0ms (1.6%)

localize8.0ms (0.3%)

series13.0ms (0.6%)

rewrite40.0ms (1.7%)

simplify11.0ms (0.5%)

prune51.0ms (2.2%)

localize8.0ms (0.4%)

series11.0ms (0.5%)

rewrite37.0ms (1.6%)

simplify11.0ms (0.4%)

prune28.0ms (1.2%)

regimes97.0ms (4.1%)

simplify2.0ms (0.1%)

end81.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11