Details

analyze304.0ms (8.7%)

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
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample952.0ms (27.1%)

Symmetry

(sort x y)

Results

856.0ms	8256×	body	128	valid
56.0ms	502×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

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

7.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.6b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.4b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	6.6b	(*.f64 y (fma.f64 z z 1))

series97.0ms (2.8%)

Counts

2 → 60

Calls

2 calls:

88.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms	(*.f64 y (fma.f64 z z 1))

rewrite60.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`
85×	`add-log-exp_binary64`

Counts

2 → 57

Calls

2 calls:

59.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
59.0ms	(*.f64 y (fma.f64 z z 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	186	22
2	2326	22
3	5603	22
0	0	0
1	0	0

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
427×	`distribute-neg-frac_binary64`
351×	`distribute-rgt-neg-in_binary64`
335×	`associate-/l*_binary64`
326×	`distribute-lft-neg-in_binary64`

Counts

117 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	993
1	140	903
2	338	901
3	1133	897
4	3155	873
5	4509	873
6	5031	873

prune77.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Error

7.0b

Counts

84 → 8

Alt Table

Status	Error	Program
	30.5b	(/.f64 (/.f64 1 x) (cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 (fma.f64 z z 1) 3))))
	25.1b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) 2)
	8.1b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) 3)
	23.5b	(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	9.5b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	7.8b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	9.2b	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 1 (fma.f64 z z 1)))
▶	7.6b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))

Compiler

Compiled 1516 to 992 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
✓	2.2b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	6.6b	(*.f64 y (fma.f64 z z 1))

series119.0ms (3.4%)

Counts

2 → 60

Calls

2 calls:

86.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
34.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))

rewrite64.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
256×	`pow2_binary64`
183×	`pow1/3_binary64`
177×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Counts

2 → 95

Calls

2 calls:

62.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
62.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	208	25
2	2513	25
3	4960	25
0	0	0
1	0	0

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

710×	`times-frac_binary64`
545×	`distribute-neg-frac_binary64`
433×	`div-sub_binary64`
378×	`sub-neg_binary64`
351×	`associate-/l*_binary64`

Counts

155 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1218
1	187	1146
2	446	1144
3	1424	1134
4	3978	1134
5	4815	1134
6	5277	1134

prune137.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	156	7	163

Error

3.1b

Counts

163 → 7

Alt Table

Status	Error	Program
▶	7.6b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	23.5b	(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	9.5b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	7.8b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	19.5b	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (.f64 (sqrt.f64 y) (hypot.f64 1 z)))
	9.2b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	8.6b	(/.f64 (/.f64 (/.f64 1 x) (fma.f64 z z 1)) y)

Compiler

Compiled 2605 to 1733 computations (33.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.6b	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
✓	2.1b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	6.6b	(*.f64 y (fma.f64 z z 1))

series89.0ms (2.5%)

Counts

1 → 36

Calls

1 calls:

89.0ms

(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)

rewrite48.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`
85×	`add-log-exp_binary64`

Counts

1 → 33

Calls

1 calls:

47.0ms

(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	186	14
2	2274	14
3	5402	14
0	0	0
1	0	0

simplify74.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

555×	`times-frac_binary64`
415×	`distribute-neg-frac_binary64`
308×	`distribute-rgt-neg-in_binary64`
306×	`associate-/l*_binary64`
297×	`div-sub_binary64`

Counts

69 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	720
1	135	720
2	340	718
3	1076	714
4	2928	684
5	4532	684
6	5033	684

prune96.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Error

3.1b

Counts

128 → 7

Alt Table

Status	Error	Program
	9.5b	(/.f64 1 (.f64 y (fma.f64 (.f64 z z) x x)))
✓	7.6b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	23.5b	(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
▶	7.8b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	19.5b	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (.f64 (sqrt.f64 y) (hypot.f64 1 z)))
	9.2b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	8.6b	(/.f64 (/.f64 (/.f64 1 x) (fma.f64 z z 1)) y)

Compiler

Compiled 2067 to 1329 computations (35.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.9b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
✓	2.0b	(.f64 (.f64 y (fma.f64 z z 1)) x)
	6.6b	(*.f64 y (fma.f64 z z 1))

series104.0ms (3%)

Counts

2 → 72

Calls

2 calls:

81.0ms	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
23.0ms	(.f64 (.f64 y (fma.f64 z z 1)) x)

rewrite48.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
157×	`log1p-udef_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

46.0ms	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
46.0ms	(.f64 (.f64 y (fma.f64 z z 1)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	180	25
2	2102	25
3	5147	25
0	0	0
1	0	0

simplify86.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

555×	`times-frac_binary64`
415×	`distribute-neg-frac_binary64`
308×	`distribute-rgt-neg-in_binary64`
306×	`associate-/l*_binary64`
297×	`div-sub_binary64`

Counts

122 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	1107
1	137	1107
2	342	1105
3	1076	1101
4	2928	1071
5	4532	1071
6	5033	1071

prune78.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Error

3.1b

Counts

111 → 7

Alt Table

Status	Error	Program
	9.5b	(/.f64 1 (.f64 y (fma.f64 (.f64 z z) x x)))
✓	7.6b	(/.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1))) x)
	23.5b	(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
✓	7.8b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	19.5b	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (.f64 (sqrt.f64 y) (hypot.f64 1 z)))
	9.2b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	8.6b	(/.f64 (/.f64 (/.f64 1 x) (fma.f64 z z 1)) y)

Compiler

Compiled 1548 to 985 computations (36.4% saved)

regimes645.0ms (18.4%)

Accuracy

Total 0.2b remaining (11.4%)

Threshold costs 0.2b (11.4%)

Counts

64 → 2

Compiler

Compiled 8507 to 6215 computations (26.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	55
1	28	55
2	27	55

end223.0ms (6.4%)

Compiler: Compiled 264 to 180 computations (31.8% saved)

Details

analyze304.0ms (8.7%)

sample952.0ms (27.1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series97.0ms (2.8%)

rewrite60.0ms (1.7%)

simplify79.0ms (2.2%)

prune77.0ms (2.2%)

localize7.0ms (0.2%)

series119.0ms (3.4%)

rewrite64.0ms (1.8%)

simplify88.0ms (2.5%)

prune137.0ms (3.9%)

localize6.0ms (0.2%)

series89.0ms (2.5%)

rewrite48.0ms (1.4%)

simplify74.0ms (2.1%)

prune96.0ms (2.7%)

localize6.0ms (0.2%)

series104.0ms (3%)

rewrite48.0ms (1.4%)

simplify86.0ms (2.4%)

prune78.0ms (2.2%)

regimes645.0ms (18.4%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end223.0ms (6.4%)

Profiling