Details

analyze356.0ms (13.1%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
37.4%	59.3%	3.3%	9
45.2%	48.4%	6.4%	10
56.9%	36.7%	6.4%	11
60.5%	30.8%	8.7%	12
64.2%	24.8%	11.1%	13
70.3%	18.6%	11.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample927.0ms (34%)

Symmetry

(sort y z)

Results

813.0ms	8256×	body	128	valid
53.0ms	586×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-def_binary64`
121×	`fma-neg_binary64`
46×	`distribute-rgt-in_binary64`
44×	`associate-r_binary64`
43×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	34	10
3	80	10
4	227	10
5	306	10
6	418	10
7	551	10
8	883	10
9	1011	10
10	1091	10
11	1111	10

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

2.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.3b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

rewrite36.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	165	10
2	2057	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

36.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
125×	`fma-neg_binary64`
50×	`associate-l_binary64`
47×	`cancel-sign-sub-inv_binary64`
42×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	338
1	32	338
2	73	338
3	153	338
4	261	338
5	410	338
6	697	338
7	831	338
8	1044	338
9	1134	338

Stop Event

1×

saturated

Counts

57 → 26

prune19.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Error

0.0b

Counts

27 → 6

Alt Table

Status	Error	Program
	11.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (+.f64 1 (*.f64 y z)))
▶	3.1b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.3b	(.f64 x (-.f64 1 (.f64 y z)))
	39.6b	(cbrt.f64 (pow.f64 (.f64 x (-.f64 1 (.f64 y z))) 3))
	32.3b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
	3.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)

Compiler

Compiled 416 to 255 computations (38.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.0b	(.f64 y (.f64 z x))

series16.0ms (0.6%)

Counts

2 → 18

Calls

2 calls:

9.0ms	(.f64 y (.f64 z x))
7.0ms	(-.f64 x (.f64 y (.f64 z x)))

rewrite63.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`expm1-log1p-u_binary64`
760×	`prod-diff_binary64`
140×	`egg-rr`
83×	`associate-r_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	154	17
2	2185	17

Stop Event

1×	node limit

Counts

2 → 140

Calls

2 calls:

59.0ms	(-.f64 x (.f64 y (.f64 z x)))
59.0ms	(.f64 y (.f64 z x))

simplify24.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

409×	`fma-def_binary64`
109×	`fma-neg_binary64`
83×	`associate-l_binary64`
55×	`distribute-rgt-in_binary64`
47×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	158
1	39	158
2	97	158
3	203	158
4	375	158
5	600	158
6	1055	158
7	1104	158
8	1176	158

Stop Event

1×

saturated

Counts

158 → 146

prune83.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	4	0	4
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Error

0.0b

Counts

152 → 4

Alt Table

Status	Error	Program
▶	6.5b	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
✓	3.1b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.3b	(.f64 x (-.f64 1 (.f64 y z)))
	33.6b	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)

Compiler

Compiled 3853 to 966 computations (74.9% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
✓	7.7b	(.f64 z (.f64 x y))

series18.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

10.0ms	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
8.0ms	(.f64 z (.f64 x y))

rewrite69.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

837×	`expm1-log1p-u_binary64`
774×	`prod-diff_binary64`
139×	`egg-rr`
85×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	179	17
2	2266	17

Stop Event

1×	node limit

Counts

2 → 139

Calls

2 calls:

65.0ms	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
65.0ms	(.f64 z (.f64 x y))

simplify38.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

412×	`fma-def_binary64`
110×	`fma-neg_binary64`
77×	`associate-l_binary64`
53×	`distribute-rgt-in_binary64`
46×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	590
1	43	590
2	102	590
3	223	590
4	386	590
5	609	590
6	1061	590
7	1110	590
8	1182	590

Stop Event

1×

saturated

Counts

211 → 147

prune72.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Error

0.0b

Counts

151 → 4

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
✓	3.1b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.3b	(.f64 x (-.f64 1 (.f64 y z)))
▶	33.6b	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)

Compiler

Compiled 3876 to 987 computations (74.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 x (.f64 z (.f64 x y))))
✓	0.0b	(-.f64 x (.f64 z (.f64 x y)))
✓	0.2b	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)
	7.7b	(.f64 z (.f64 x y))

series194.0ms (7.1%)

Counts

3 → 52

Calls

3 calls:

135.0ms	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)
52.0ms	(sqrt.f64 (-.f64 x (.f64 z (.f64 x y))))
7.0ms	(-.f64 x (.f64 z (.f64 x y)))

rewrite119.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`prod-diff_binary64`
394×	`egg-rr`
260×	`fma-def_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	218	32
2	2623	32

Stop Event

1×	node limit

Counts

3 → 394

Calls

3 calls:

109.0ms	(sqrt.f64 (-.f64 x (.f64 z (.f64 x y))))
109.0ms	(-.f64 x (.f64 z (.f64 x y)))
109.0ms	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)

simplify55.0ms (2%)

Algorithm

1×	egg-herbie

Rules

453×	`distribute-rgt-neg-in_binary64`
447×	`distribute-lft-neg-in_binary64`
404×	`fma-neg_binary64`
281×	`associate-r_binary64`
278×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	616
1	124	604
2	401	586
3	1946	566
4	4550	566

Stop Event

1×	node limit

Counts

446 → 227

prune112.0ms (4.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	241	4	245

Error

0.0b

Counts

245 → 4

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 x (pow.f64 (.f64 z (.f64 x y)) 1))
✓	3.1b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.3b	(.f64 x (-.f64 1 (.f64 y z)))
✓	33.6b	(pow.f64 (sqrt.f64 (-.f64 x (.f64 z (.f64 x y)))) 2)

Compiler

Compiled 6079 to 1457 computations (76% saved)

regimes201.0ms (7.4%)

Accuracy

Total 2.5b remaining (99.1%)

Threshold costs 0b (0%)

Counts

22 → 3

Compiler

Compiled 1814 to 1200 computations (33.8% saved)

bsearch18.0ms (0.6%)

Steps

Iters	Range		Point
6	2.8783060209760683e-210	3.03180196832033e-209	1.0343249380691399e-209
2	-3.8242193825268484e-119	-1.4140353554826367e-120	-1.6898890574526774e-119

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	43
1	37	43
2	55	43
3	70	43
4	79	43
5	83	43
6	84	43

Stop Event

1×

saturated

end215.0ms (7.9%)

Compiler: Compiled 177 to 106 computations (40.1% saved)

Details

analyze356.0ms (13.1%)

sample927.0ms (34%)

simplify18.0ms (0.6%)

prune1.0ms (0.1%)

localize7.0ms (0.2%)

series8.0ms (0.3%)

rewrite36.0ms (1.3%)

simplify29.0ms (1%)

prune19.0ms (0.7%)

localize5.0ms (0.2%)

series16.0ms (0.6%)

rewrite63.0ms (2.3%)

simplify24.0ms (0.9%)

prune83.0ms (3%)

localize7.0ms (0.3%)

series18.0ms (0.7%)

rewrite69.0ms (2.5%)

simplify38.0ms (1.4%)

prune72.0ms (2.7%)

localize10.0ms (0.4%)

series194.0ms (7.1%)

rewrite119.0ms (4.4%)

simplify55.0ms (2%)

prune112.0ms (4.1%)

regimes201.0ms (7.4%)

bsearch18.0ms (0.6%)

simplify4.0ms (0.1%)

end215.0ms (7.9%)

Profiling