Details

analyze875.0ms (13.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
18.7%	70.2%	11.1%	11
21.1%	66.7%	12.3%	12
31.6%	55.9%	12.5%	13
34.5%	52.3%	13.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (16.9%)

Results

885.0ms	8256×	body	128	valid
197.0ms	1877×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`fma-def_binary64`
8×	`+-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	25	9
3	38	9
4	52	9
5	52	9

prune3.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (fma.f64 x y z) t)
▶	0.1b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)

Compiler

Compiled 68 to 38 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x y) z)
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
✓	0.1b	(.f64 (+.f64 (.f64 x y) z) y)

series30.0ms (0.4%)

Counts

3 → 120

Calls

3 calls:

17.0ms	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
8.0ms	(.f64 (+.f64 (.f64 x y) z) y)
4.0ms	(+.f64 (*.f64 x y) z)

rewrite60.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
465×	`fma-def_binary64`
231×	`fma-neg_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

3 → 139

Calls

3 calls:

57.0ms	(+.f64 (*.f64 x y) z)
57.0ms	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
57.0ms	(.f64 (+.f64 (.f64 x y) z) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	199	22
2	2649	22
3	5286	22
0	0	0
1	0	0

simplify172.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

804×	`sqr-pow_binary64`
546×	`associate-l_binary64`
512×	`fma-def_binary64`
492×	`fabs-mul_binary64`
489×	`cube-prod_binary64`

Counts

259 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	1061
1	35	993
2	52	870
3	84	804
4	161	804
5	369	804
6	1070	804
7	1792	804
8	1930	804
9	2086	804
10	2266	804
11	2447	804
12	2660	804
13	2849	804
14	3269	804
15	3834	804
16	4520	804
17	4738	804
18	4683	804

prune117.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	6	158

Error

Counts

158 → 6

Alt Table

Status	Error	Program
	30.1b	(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (fma.f64 x y z)) t)
	3.0b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)
▶	0.1b	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
	6.4b	(fma.f64 (.f64 (fma.f64 x y z) (cbrt.f64 (.f64 y y))) (cbrt.f64 y) t)
	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
	27.1b	(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x y z) 3)) y) t)

Compiler

Compiled 2341 to 805 computations (65.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
✓	0.1b	(fma.f64 y (.f64 x y) (.f64 y z))

series23.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

14.0ms	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
9.0ms	(fma.f64 y (.f64 x y) (.f64 y z))

rewrite110.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

739×	`prod-diff_binary64`
505×	`fma-udef_binary64`
376×	`fma-def_binary64`
209×	`fma-neg_binary64`
178×	`expm1-udef_binary64`

Counts

2 → 84

Calls

2 calls:

108.0ms	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
108.0ms	(fma.f64 y (.f64 x y) (.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	188	23
2	2381	17
3	4754	17
4	4729	17
5	5054	17
0	0	0
1	0	0

simplify163.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

804×	`sqr-pow_binary64`
547×	`associate-l_binary64`
513×	`fma-def_binary64`
492×	`fabs-mul_binary64`
489×	`cube-prod_binary64`

Counts

168 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	902
1	30	834
2	48	804
3	83	645
4	161	645
5	369	645
6	1070	645
7	1792	645
8	1930	645
9	2086	645
10	2266	645
11	2447	645
12	2660	645
13	2849	645
14	3269	645
15	3834	645
16	4520	645
17	4738	645
18	4683	645

prune64.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Error

Counts

102 → 6

Alt Table

Status	Error	Program
	3.0b	(fma.f64 (*.f64 y y) x (fma.f64 y z t))
✓	0.1b	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
	6.4b	(fma.f64 (.f64 (fma.f64 x y z) (cbrt.f64 (.f64 y y))) (cbrt.f64 y) t)
	30.1b	(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (fma.f64 x y z)) t)
▶	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
	27.1b	(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x y z) 3)) y) t)

Compiler

Compiled 1513 to 458 computations (69.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 x y z)) y)
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x y z)) 2)
✓	0.6b	(cbrt.f64 (fma.f64 x y z))

series2.1s (31.7%)

Counts

4 → 156

Calls

4 calls:

2.0s	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
49.0ms	(pow.f64 (cbrt.f64 (fma.f64 x y z)) 2)
42.0ms	(*.f64 (cbrt.f64 (fma.f64 x y z)) y)
33.0ms	(cbrt.f64 (fma.f64 x y z))

rewrite58.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

897×	`log1p-expm1-u_binary64`
897×	`expm1-log1p-u_binary64`
138×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

56.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
56.0ms	(*.f64 (cbrt.f64 (fma.f64 x y z)) y)
56.0ms	(pow.f64 (cbrt.f64 (fma.f64 x y z)) 2)
56.0ms	(cbrt.f64 (fma.f64 x y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	218	38
2	2349	38
3	5693	38
0	0	0
1	0	0

simplify152.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

429×	`times-frac_binary64`
372×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
350×	`fma-def_binary64`
344×	`associate-l_binary64`

Counts

238 → 274

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	474	7771
1	1615	7399
2	5069	7399

prune551.0ms (8.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	351	6	357

Error

Counts

357 → 6

Alt Table

Status	Error	Program
▶	3.0b	(fma.f64 (*.f64 y y) x (fma.f64 y z t))
✓	0.1b	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
	6.4b	(fma.f64 (.f64 (fma.f64 x y z) (cbrt.f64 (.f64 y y))) (cbrt.f64 y) t)
	30.1b	(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (fma.f64 x y z)) t)
✓	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
	27.1b	(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x y z) 3)) y) t)

Compiler

Compiled 14144 to 7816 computations (44.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.8b	(fma.f64 (*.f64 y y) x (fma.f64 y z t))

series20.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

20.0ms

(fma.f64 (*.f64 y y) x (fma.f64 y z t))

rewrite70.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

685×	`log1p-expm1-u_binary64`
685×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
128×	`prod-diff_binary64`

Counts

1 → 25

Calls

1 calls:

69.0ms

(fma.f64 (*.f64 y y) x (fma.f64 y z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	158	12
2	1781	12
3	4936	12
4	4962	12
0	0	0
1	0	0

simplify146.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

804×	`sqr-pow_binary64`
547×	`associate-l_binary64`
513×	`fma-def_binary64`
492×	`fabs-mul_binary64`
489×	`cube-prod_binary64`

Counts

73 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	554
1	30	486
2	48	483
3	83	378
4	161	378
5	369	378
6	1070	378
7	1792	378
8	1930	378
9	2086	378
10	2266	378
11	2447	378
12	2660	378
13	2849	378
14	3269	378
15	3834	378
16	4520	378
17	4738	378
18	4683	378

prune102.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	38	6	44

Error

Counts

44 → 6

Alt Table

Status	Error	Program
✓	3.0b	(fma.f64 (*.f64 y y) x (fma.f64 y z t))
✓	0.1b	(+.f64 (fma.f64 y (.f64 x y) (.f64 y z)) t)
	6.4b	(fma.f64 (.f64 (fma.f64 x y z) (cbrt.f64 (.f64 y y))) (cbrt.f64 y) t)
	30.1b	(fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (fma.f64 x y z)) t)
✓	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y z)) 2) (*.f64 (cbrt.f64 (fma.f64 x y z)) y) t)
	27.1b	(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x y z) 3)) y) t)

Compiler

Compiled 545 to 159 computations (70.8% saved)

regimes547.0ms (8.3%)

Accuracy

Total 0.0b remaining (75.8%)

Threshold costs 0.0b (75.8%)

Counts

78 → 1

Compiler

Compiled 6416 to 3934 computations (38.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	14	15
2	13	15

end83.0ms (1.3%)

Compiler: Compiled 124 to 71 computations (42.7% saved)

Details

analyze875.0ms (13.3%)

sample1.1s (16.9%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series30.0ms (0.4%)

rewrite60.0ms (0.9%)

simplify172.0ms (2.6%)

prune117.0ms (1.8%)

localize6.0ms (0.1%)

series23.0ms (0.4%)

rewrite110.0ms (1.7%)

simplify163.0ms (2.5%)

prune64.0ms (1%)

localize10.0ms (0.2%)

series2.1s (31.7%)

rewrite58.0ms (0.9%)

simplify152.0ms (2.3%)

prune551.0ms (8.4%)

localize6.0ms (0.1%)

series20.0ms (0.3%)

rewrite70.0ms (1.1%)

simplify146.0ms (2.2%)

prune102.0ms (1.5%)

regimes547.0ms (8.3%)

simplify2.0ms (0%)

end83.0ms (1.3%)

Profiling