Details

analyze875.0ms (22.8%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (29.2%)

Results

845.0ms	8256×	body	128	valid
224.0ms	2188×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-def_binary64`
751×	`fma-neg_binary64`
237×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	67	11
4	143	11
5	294	11
6	631	11
7	1210	11
8	2505	11
9	3568	11
10	3915	11
11	3964	11
12	3994	11
13	3999	11
14	3999	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

rewrite39.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

38.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
715×	`fma-neg_binary64`
244×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	69	561
2	162	552
3	383	552
4	825	480
5	1519	480
6	2510	480
7	3538	480
8	3588	480
9	3632	480
10	3690	480
11	3690	480

Stop Event

1×

saturated

Counts

77 → 42

prune26.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

0.0b

Counts

44 → 4

Alt Table

Status	Error	Program
	37.0b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	4.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)

Compiler

Compiled 630 to 189 computations (70% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	5.0b	(/.f64 (*.f64 z x) t)
✓	5.3b	(/.f64 (*.f64 y z) t)

series64.0ms (1.7%)

Counts

4 → 24

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
15.0ms	(/.f64 (*.f64 y z) t)
15.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
11.0ms	(/.f64 (*.f64 z x) t)

rewrite74.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`fma-neg_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
181×	`egg-rr`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	254	43
2	4150	43

Stop Event

1×	node limit

Counts

4 → 181

Calls

4 calls:

70.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
70.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
70.0ms	(/.f64 (*.f64 z x) t)
70.0ms	(/.f64 (*.f64 y z) t)

simplify48.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
498×	`fma-neg_binary64`
196×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-in_binary64`
137×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	141
1	64	141
2	154	132
3	361	132
4	751	132
5	1285	132
6	2173	132
7	3160	132
8	3201	132
9	3243	132
10	3301	132
11	3301	132

Stop Event

1×

saturated

Counts

205 → 192

prune129.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	189	7	196

Error

0.0b

Counts

196 → 7

Alt Table

Status	Error	Program
	4.9b	(-.f64 (fma.f64 (.f64 y z) (/.f64 1 t) x) (/.f64 (.f64 z x) t))
	35.1b	(-.f64 (+.f64 (.f64 (/.f64 z (sqrt.f64 t)) (/.f64 y (sqrt.f64 t))) x) (/.f64 (.f64 z x) t))
	7.9b	(+.f64 (*.f64 (/.f64 y t) z) (-.f64 x (/.f64 z (/.f64 t x))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	4.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
	4.9b	(-.f64 (+.f64 (pow.f64 (/.f64 t (.f64 y z)) -1) x) (/.f64 (.f64 z x) t))
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)

Compiler

Compiled 4275 to 1104 computations (74.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
✓	0.2b	(*.f64 z (/.f64 1 t))
✓	3.6b	(.f64 x (.f64 z (/.f64 1 t)))
	5.3b	(/.f64 (*.f64 y z) t)

series41.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
13.0ms	(.f64 x (.f64 z (/.f64 1 t)))
5.0ms	(*.f64 z (/.f64 1 t))

rewrite66.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`add-cbrt-cube_binary64`
141×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	293	30
2	4398	30

Stop Event

1×	node limit

Counts

3 → 93

Calls

3 calls:

65.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
64.0ms	(*.f64 z (/.f64 1 t))
64.0ms	(.f64 x (.f64 z (/.f64 1 t)))

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
716×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	1125
1	69	909
2	162	900
3	384	900
4	826	828
5	1520	828
6	2532	828
7	3559	828
8	3609	828
9	3653	828
10	3711	828
11	3711	828

Stop Event

1×

saturated

Counts

201 → 108

prune119.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	149	8	157

Error

0.0b

Counts

157 → 8

Alt Table

Status	Error	Program
▶	4.3b	(fma.f64 (.f64 z y) (/.f64 1 t) (.f64 x (-.f64 1 (/.f64 z t))))
	35.1b	(-.f64 (+.f64 (.f64 (/.f64 z (sqrt.f64 t)) (/.f64 y (sqrt.f64 t))) x) (/.f64 (.f64 z x) t))
	7.9b	(+.f64 (*.f64 (/.f64 y t) z) (-.f64 x (/.f64 z (/.f64 t x))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	4.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
	4.9b	(-.f64 (+.f64 (pow.f64 (/.f64 t (.f64 y z)) -1) x) (/.f64 (.f64 z x) t))
	8.6b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)

Compiler

Compiled 3140 to 1144 computations (63.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.3b	(*.f64 x (-.f64 1 (/.f64 z t)))
✓	2.9b	(fma.f64 (.f64 z y) (/.f64 1 t) (.f64 x (-.f64 1 (/.f64 z t))))

series34.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

23.0ms	(fma.f64 (.f64 z y) (/.f64 1 t) (.f64 x (-.f64 1 (/.f64 z t))))
11.0ms	(*.f64 x (-.f64 1 (/.f64 z t)))

rewrite49.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
225×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
117×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	252	29
2	3262	29

Stop Event

1×	node limit

Counts

2 → 44

Calls

2 calls:

47.0ms	(*.f64 x (-.f64 1 (/.f64 z t)))
47.0ms	(fma.f64 (.f64 z y) (/.f64 1 t) (.f64 x (-.f64 1 (/.f64 z t))))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
714×	`fma-neg_binary64`
183×	`cancel-sign-sub-inv_binary64`
155×	`distribute-rgt-in_binary64`
99×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	1107
1	73	891
2	170	882
3	403	882
4	853	810
5	1582	810
6	2600	810
7	3399	810
8	3447	810
9	3491	810
10	3549	810
11	3549	810

Stop Event

1×

saturated

Counts

128 → 59

prune43.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	59	8	67

Error

Counts

67 → 8

Alt Table

Status	Error	Program
	10.8b	(fma.f64 (.f64 z y) (/.f64 1 t) (/.f64 (.f64 (-.f64 1 (pow.f64 (/.f64 z t) 2)) x) (+.f64 1 (/.f64 z t))))
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
	35.1b	(-.f64 (+.f64 (.f64 (/.f64 z (sqrt.f64 t)) (/.f64 y (sqrt.f64 t))) x) (/.f64 (.f64 z x) t))
	7.9b	(+.f64 (*.f64 (/.f64 y t) z) (-.f64 x (/.f64 z (/.f64 t x))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	4.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (.f64 x (*.f64 z (/.f64 1 t))))
	4.9b	(-.f64 (+.f64 (pow.f64 (/.f64 t (.f64 y z)) -1) x) (/.f64 (.f64 z x) t))
	8.6b	(fma.f64 z (/.f64 (-.f64 y x) t) x)

Compiler

Compiled 1115 to 518 computations (53.5% saved)

regimes652.0ms (17%)

Accuracy

Total 1.0b remaining (98.6%)

Threshold costs 1.0b (98.6%)

Counts

70 → 3

Compiler

Compiled 6026 to 3768 computations (37.5% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	98
1	48	98
2	71	98
3	85	98
4	93	98
5	95	98

Stop Event

1×

saturated

end111.0ms (2.9%)

Compiler: Compiled 283 to 155 computations (45.2% saved)

Details

analyze875.0ms (22.8%)

sample1.1s (29.2%)

simplify63.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series16.0ms (0.4%)

rewrite39.0ms (1%)

simplify68.0ms (1.8%)

prune26.0ms (0.7%)

localize8.0ms (0.2%)

series64.0ms (1.7%)

rewrite74.0ms (1.9%)

simplify48.0ms (1.2%)

prune129.0ms (3.3%)

localize9.0ms (0.2%)

series41.0ms (1.1%)

rewrite66.0ms (1.7%)

simplify84.0ms (2.2%)

prune119.0ms (3.1%)

localize8.0ms (0.2%)

series34.0ms (0.9%)

rewrite49.0ms (1.3%)

simplify80.0ms (2.1%)

prune43.0ms (1.1%)

regimes652.0ms (17%)

bsearch2.0ms (0.1%)

simplify6.0ms (0.2%)

end111.0ms (2.9%)

Profiling