Details

analyze1.2s (21.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
16.4%	83.4%	0.2%	11
19.9%	79.9%	0.2%	12
21.6%	77.2%	1.2%	13
24.8%	73.7%	1.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (26.2%)

Symmetry

(sort x y)

(sort z t)

Results

974.0ms	8256×	body	128	valid
390.0ms	3101×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
389×	`fma-neg_binary64`
131×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	46	13
3	77	13
4	161	13
5	292	13
6	483	13
7	733	13
8	1186	13
9	1758	13
10	2658	13
11	2745	13
12	2775	13
13	2780	13

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

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

8.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 x y) (.f64 z t))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series38.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

27.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
10.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite69.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

420×	`fma-def_binary64`
224×	`egg-rr`
220×	`fma-neg_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	227	23
2	3300	23

Stop Event

1×	node limit

Counts

2 → 224

Calls

2 calls:

65.0ms	(-.f64 (.f64 x y) (.f64 z t))
65.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1168×	`fma-def_binary64`
351×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
93×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1140
1	49	1140
2	108	1140
3	245	1140
4	520	1140
5	988	1140
6	1828	1140
7	2773	1140
8	3029	1140
9	3067	1140
10	3072	1140

Stop Event

1×

saturated

Counts

332 → 237

prune147.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	230	7	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

Status	Error	Program
▶	7.1b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
	34.2b	(*.f64 y (/.f64 x a))
	27.6b	(*.f64 t (/.f64 (neg.f64 z) a))
	7.9b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 a) 2)) (/.f64 x (cbrt.f64 a)) (neg.f64 (/.f64 z (/.f64 a t))))
	8.3b	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)
	8.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	8.0b	(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)

Compiler

Compiled 4749 to 1204 computations (74.6% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
✓	5.2b	(/.f64 z (/.f64 a t))

series42.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

29.0ms	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
13.0ms	(/.f64 z (/.f64 a t))

rewrite169.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`prod-diff_binary64`
548×	`egg-rr`
217×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`
120×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	281	21
2	3649	21

Stop Event

1×	node limit

Counts

2 → 548

Calls

2 calls:

149.0ms	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
149.0ms	(/.f64 z (/.f64 a t))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1163×	`fma-def_binary64`
349×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
92×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	972
1	46	972
2	105	972
3	240	972
4	516	972
5	982	972
6	1825	972
7	2780	972
8	3036	972
9	3074	972
10	3079	972

Stop Event

1×

saturated

Counts

644 → 556

prune317.0ms (5.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	554	2	556
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	556	7	563

Error

0.0b

Counts

563 → 7

Alt Table

Status	Error	Program
	8.0b	(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)
	34.3b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (/.f64 a t))) (/.f64 z (sqrt.f64 (/.f64 a t))))))
✓	7.1b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
	34.2b	(*.f64 y (/.f64 x a))
	27.6b	(*.f64 t (/.f64 (neg.f64 z) a))
	8.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
▶	7.1b	(-.f64 (/.f64 x (/.f64 a y)) (*.f64 z (/.f64 t a)))

Compiler

Compiled 20985 to 4881 computations (76.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (/.f64 a y)) (*.f64 z (/.f64 t a)))
✓	4.8b	(/.f64 x (/.f64 a y))
✓	5.2b	(*.f64 z (/.f64 t a))

series53.0ms (1%)

Counts

3 → 132

Calls

3 calls:

28.0ms	(-.f64 (/.f64 x (/.f64 a y)) (*.f64 z (/.f64 t a)))
13.0ms	(/.f64 x (/.f64 a y))
12.0ms	(*.f64 z (/.f64 t a))

rewrite70.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`fma-def_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
195×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	251	30
2	3894	30

Stop Event

1×	node limit

Counts

3 → 195

Calls

3 calls:

66.0ms	(-.f64 (/.f64 x (/.f64 a y)) (*.f64 z (/.f64 t a)))
66.0ms	(/.f64 x (/.f64 a y))
66.0ms	(*.f64 z (/.f64 t a))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1163×	`fma-def_binary64`
320×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
92×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	1224
1	46	1224
2	105	1224
3	240	1224
4	514	1224
5	980	1224
6	1792	1224
7	2745	1224
8	3001	1224
9	3039	1224
10	3044	1224

Stop Event

1×

saturated

Counts

327 → 203

prune128.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	202	8	210

Error

0.0b

Counts

210 → 8

Alt Table

Status	Error	Program
	27.6b	(*.f64 t (/.f64 (neg.f64 z) a))
	16.3b	(-.f64 (.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 a y) 2))) (/.f64 x (cbrt.f64 (/.f64 a y)))) (.f64 z (/.f64 t a)))
▶	8.0b	(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)
	34.3b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (/.f64 a t))) (/.f64 z (sqrt.f64 (/.f64 a t))))))
✓	7.1b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))
	34.2b	(*.f64 y (/.f64 x a))
	8.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
✓	7.1b	(-.f64 (/.f64 x (/.f64 a y)) (*.f64 z (/.f64 t a)))

Compiler

Compiled 4273 to 1034 computations (75.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.5b	(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)

series28.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

28.0ms

(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

894×	`log1p-expm1-u_binary64`
894×	`expm1-log1p-u_binary64`
224×	`prod-diff_binary64`
108×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	207	11
2	2726	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

42.0ms

(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1163×	`fma-def_binary64`
349×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
92×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	720
1	46	720
2	105	720
3	240	720
4	516	720
5	982	720
6	1825	720
7	2781	720
8	3037	720
9	3075	720
10	3080	720

Stop Event

1×

saturated

Counts

93 → 40

prune25.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	41	7	48

Error

Counts

48 → 7

Alt Table

Status	Error	Program
	27.6b	(*.f64 t (/.f64 (neg.f64 z) a))
	16.3b	(-.f64 (.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 a y) 2))) (/.f64 x (cbrt.f64 (/.f64 a y)))) (.f64 z (/.f64 t a)))
	8.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	34.4b	(/.f64 y (/.f64 a x))
✓	8.0b	(/.f64 (fma.f64 x y (*.f64 z (neg.f64 t))) a)
	34.3b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (/.f64 a t))) (/.f64 z (sqrt.f64 (/.f64 a t))))))
✓	7.1b	(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 z (/.f64 a t))))

Compiler

Compiled 648 to 226 computations (65.1% saved)

regimes1.1s (19.4%)

Accuracy

Total 0.6b remaining (95.8%)

Threshold costs 0.6b (95.8%)

Counts

63 → 3

Compiler

Compiled 11224 to 7105 computations (36.7% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	75
1	53	75
2	65	75
3	72	75
4	74	75

Stop Event

1×

saturated

end257.0ms (4.7%)

Remove: (sort z t)
Compiler: Compiled 569 to 288 computations (49.4% saved)

Details

analyze1.2s (21.6%)

sample1.4s (26.2%)

simplify33.0ms (0.6%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series38.0ms (0.7%)

rewrite69.0ms (1.3%)

simplify81.0ms (1.5%)

prune147.0ms (2.7%)

localize11.0ms (0.2%)

series42.0ms (0.8%)

rewrite169.0ms (3.1%)

simplify93.0ms (1.7%)

prune317.0ms (5.8%)

localize7.0ms (0.1%)

series53.0ms (1%)

rewrite70.0ms (1.3%)

simplify89.0ms (1.6%)

prune128.0ms (2.4%)

localize6.0ms (0.1%)

series28.0ms (0.5%)

rewrite43.0ms (0.8%)

simplify66.0ms (1.2%)

prune25.0ms (0.5%)

regimes1.1s (19.4%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end257.0ms (4.7%)

Profiling