Details

analyze1.1s (28.6%)

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
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.2%	66.5%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample72.0ms (1.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	28×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify113.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

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
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series57.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

36.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
21.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify93.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune116.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Error

0.0b

Counts

137 → 5

Alt Table

Status	Error	Program
	26.3b	(fma.f64 (/.f64 y a) t x)
	40.2b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	6.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

Compiler

Compiled 3386 to 1111 computations (67.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

series67.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

38.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
20.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
8.0ms	(/.f64 1 (-.f64 z a))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

13.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
4.0ms	(/.f64 1 (-.f64 z a))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

simplify137.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

717×	`times-frac_binary64`
517×	`cancel-sign-sub-inv_binary64`
449×	`fma-neg_binary64`
361×	`sub-neg_binary64`
182×	`+-commutative_binary64`

Counts

225 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	4920
1	748	4681
2	2739	4633
3	4920	4632
4	5192	4632

prune162.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	225	6	231

Error

Counts

231 → 6

Alt Table

Status	Error	Program
	26.3b	(fma.f64 (/.f64 y a) t x)
	33.2b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)) (sqrt.f64 (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)))
	40.2b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	6.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

Compiler

Compiled 5347 to 1989 computations (62.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	2.1b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	5.3b	(/.f64 (*.f64 y t) (-.f64 z a))

series122.0ms (3.1%)

Counts

4 → 156

Calls

4 calls:

51.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
28.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
23.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
20.0ms	(/.f64 y (-.f64 z a))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
33×	`prod-diff_binary64`

Counts

4 → 141

Calls

4 calls:

9.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
5.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
4.0ms	(/.f64 y (-.f64 z a))
0.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify222.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

540×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
252×	`sub-neg_binary64`
206×	`associate-/l*_binary64`
189×	`times-frac_binary64`

Counts

297 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7851
1	956	7082
2	3439	6648
3	4776	6648
4	4997	6648
5	4858	6648

prune183.0ms (4.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Status	Error	Program
▶	26.3b	(fma.f64 (/.f64 y a) t x)
	33.2b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)) (sqrt.f64 (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)))
	40.2b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	6.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

Compiler

Compiled 8623 to 1800 computations (79.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.0b	(fma.f64 (/.f64 y a) t x)

series15.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(fma.f64 (/.f64 y a) t x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y a) t x)

simplify93.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

601×	`distribute-rgt-out_binary64`
552×	`distribute-rgt-in_binary64`
546×	`associate-*l/_binary64`
522×	`distribute-lft-in_binary64`
416×	`times-frac_binary64`

Counts

58 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	463
1	26	446
2	51	446
3	134	446
4	445	446
5	1651	446
6	4002	446
7	4440	446
8	4739	446
9	5000	446
10	4982	446

prune13.0ms (0.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	22	6	28

Error

Counts

28 → 6

Alt Table

Status	Error	Program
✓	26.3b	(fma.f64 (/.f64 y a) t x)
	33.2b	(.f64 (sqrt.f64 (fma.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)) (sqrt.f64 (fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)))
	40.2b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	6.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

Compiler

Compiled 368 to 131 computations (64.4% saved)

regimes380.0ms (9.7%)

Accuracy

Total 1.4b remaining (98.6%)

Threshold costs 0b (0%)

Counts

57 → 1

Compiler

Compiled 6911 to 4251 computations (38.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	25	20
3	31	20
4	35	20
5	36	20
6	36	20

end0.0ms (0%)

Compiler: Compiled 19 to 10 computations (47.4% saved)

sample828.0ms (21.2%)

Algorithm

1×

intervals

Results

367.0ms	7999×	body	128	valid
31.0ms	694×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 185 to 106 computations (42.7% saved)

Details

analyze1.1s (28.6%)

sample72.0ms (1.8%)

simplify113.0ms (2.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series57.0ms (1.5%)

rewrite12.0ms (0.3%)

simplify93.0ms (2.4%)

prune116.0ms (3%)

localize10.0ms (0.2%)

series67.0ms (1.7%)

rewrite23.0ms (0.6%)

simplify137.0ms (3.5%)

prune162.0ms (4.2%)

localize9.0ms (0.2%)

series122.0ms (3.1%)

rewrite38.0ms (1%)

simplify222.0ms (5.7%)

prune183.0ms (4.7%)

localize5.0ms (0.1%)

series15.0ms (0.4%)

rewrite1.0ms (0%)

simplify93.0ms (2.4%)

prune13.0ms (0.3%)

regimes380.0ms (9.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample828.0ms (21.2%)

Profiling