Details

analyze1.8s (28.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.8s (29.7%)

Results

1.2s	8256×	body	128	valid
569.0ms	3842×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
21×	`associate-+r+_binary64`
18×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	69	15
3	147	13
4	192	13
5	204	13
6	207	13

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	6.0b	(.f64 (.f64 a z) b)

series59.0ms (1%)

Counts

4 → 204

Calls

4 calls:

24.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
23.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
8.0ms	(.f64 (.f64 a z) b)
4.0ms	(+.f64 x (*.f64 y z))

rewrite74.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	311	37
2	4617	37

Stop Event

1×	node limit

Counts

4 → 135

Calls

4 calls:

71.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
71.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
71.0ms	(+.f64 x (*.f64 y z))
71.0ms	(.f64 (.f64 a z) b)

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
16×	`associate-+l+_binary64`
14×	`associate-+r+_binary64`
13×	`+-commutative_binary64`
9×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1867
1	80	1695
2	144	1693
3	183	1693

Stop Event

1×

saturated

Counts

339 → 160

prune108.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3))
	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 3409 to 817 computations (76% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z y x))
✓	2.6b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

series45.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 a t (fma.f64 z y x))
22.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
202×	`prod-diff_binary64`
193×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	217	25
2	2636	25

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

46.0ms	(fma.f64 a t (fma.f64 z y x))
46.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
16×	`associate-+l+_binary64`
14×	`associate-+r+_binary64`
13×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	1395
1	81	1284
2	144	1282
3	183	1282

Stop Event

1×

saturated

Counts

192 → 87

prune52.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Error

Counts

91 → 4

Alt Table

Status	Error	Program
	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3))
▶	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 1463 to 337 computations (77% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.6b	(fma.f64 a (fma.f64 z b t) x)

series37.0ms (0.6%)

Counts

2 → 132

Calls

2 calls:

22.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
15.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
192×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	197	22
2	2375	22

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

43.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
43.0ms	(fma.f64 a (fma.f64 z b t) x)

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

87×	`fma-def_binary64`
16×	`+-commutative_binary64`
15×	`associate-+l+_binary64`
12×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	1561
1	89	1301
2	156	1301
3	187	1301

Stop Event

1×

saturated

Counts

179 → 77

prune49.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	77	4	81

Error

Counts

81 → 4

Alt Table

Status	Error	Program
▶	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3))
✓	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 1120 to 288 computations (74.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (*.f64 y z))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3)
✓	4.8b	(.f64 a (.f64 z b))
✓	13.8b	(cbrt.f64 (.f64 a (.f64 z b)))

series1.1s (18.5%)

Counts

3 → 88

Calls

3 calls:

585.0ms	(pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3)
550.0ms	(cbrt.f64 (.f64 a (.f64 z b)))
8.0ms	(.f64 a (.f64 z b))

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`log1p-expm1-u_binary64`
707×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
84×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	181	23
2	1987	23

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

49.0ms	(pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3)
48.0ms	(.f64 a (.f64 z b))
48.0ms	(cbrt.f64 (.f64 a (.f64 z b)))

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

566×	`associate-l_binary64`
461×	`associate-r_binary64`
434×	`fma-def_binary64`
196×	`distribute-rgt-in_binary64`
163×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1492
1	237	1240
2	544	1192
3	1539	844

Stop Event

1×	node limit

Counts

172 → 95

prune97.0ms (1.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (cbrt.f64 (.f64 a (.f64 z b))) 3))
✓	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 3223 to 1018 computations (68.4% saved)

regimes489.0ms (7.9%)

Accuracy

Total 1.5b remaining (98.7%)

Threshold costs 0b (0%)

Counts

61 → 2

Compiler

Compiled 6860 to 4396 computations (35.9% saved)

bsearch8.0ms (0.1%)

Steps

Iters	Range		Point
1	-4.3940222235769175e-155	-5.195290757860631e-157	-4.6166139872620714e-156

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	21	37

Stop Event

1×

saturated

end71.0ms (1.1%)

Compiler: Compiled 145 to 80 computations (44.8% saved)

Details

analyze1.8s (28.6%)

sample1.8s (29.7%)

simplify12.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series59.0ms (1%)

rewrite74.0ms (1.2%)

simplify38.0ms (0.6%)

prune108.0ms (1.7%)

localize15.0ms (0.2%)

series45.0ms (0.7%)

rewrite47.0ms (0.8%)

simplify30.0ms (0.5%)

prune52.0ms (0.8%)

localize8.0ms (0.1%)

series37.0ms (0.6%)

rewrite44.0ms (0.7%)

simplify33.0ms (0.5%)

prune49.0ms (0.8%)

localize14.0ms (0.2%)

series1.1s (18.5%)

rewrite50.0ms (0.8%)

simplify45.0ms (0.7%)

prune97.0ms (1.6%)

regimes489.0ms (7.9%)

bsearch8.0ms (0.1%)

simplify2.0ms (0%)

end71.0ms (1.1%)

Profiling