Details

analyze1.3s (23.3%)

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
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (26.7%)

Results

970.0ms	7032×	body	128	valid
161.0ms	472×	body	512	valid
136.0ms	347×	body	1024	valid
88.0ms	670×	body	128	invalid
82.0ms	347×	body	256	valid
36.0ms	58×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify130.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

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

9.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.3b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.2b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series74.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

53.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.2%)

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

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune123.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	26.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y a) t))
	29.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
▶	10.4b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	24.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))

Compiler

Compiled 3576 to 1200 computations (66.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
✓	3.5b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

series74.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

43.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
22.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
9.0ms	(/.f64 1 (-.f64 a t))

rewrite23.0ms (0.4%)

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:

12.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

simplify141.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

699×	`times-frac_binary64`
529×	`cancel-sign-sub-inv_binary64`
521×	`fma-neg_binary64`
400×	`sub-neg_binary64`
187×	`+-commutative_binary64`

Counts

225 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	5043
1	793	4777
2	2825	4721
3	4910	4720
4	5185	4720

prune150.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	230	6	236

Error

0.0b

Counts

236 → 6

Alt Table

Status	Error	Program
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	26.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y a) t))
	29.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
✓	10.4b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
▶	24.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))

Compiler

Compiled 5782 to 2010 computations (65.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	6.6b	(*.f64 (/.f64 y t) (-.f64 z a))

series53.0ms (0.9%)

Counts

2 → 108

Calls

2 calls:

34.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
19.0ms	(*.f64 (/.f64 y t) (-.f64 z a))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 108

Calls

2 calls:

8.0ms	(*.f64 (/.f64 y t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

simplify125.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
488×	`distribute-rgt-in_binary64`
459×	`distribute-lft-in_binary64`
280×	`fma-neg_binary64`
153×	`exp-prod_binary64`

Counts

216 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3204
1	473	2592
2	1528	2538
3	4618	2538
4	5000	2538
5	4948	2538

prune126.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	177	7	184

Error

0.0b

Counts

184 → 7

Alt Table

Status	Error	Program
✓	24.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 z a) y) t))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	24.7b	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))
	29.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
✓	10.4b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))

Compiler

Compiled 3728 to 894 computations (76% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))
✓	0.2b	(*.f64 (/.f64 1 t) (-.f64 z a))
✓	4.2b	(.f64 y (.f64 (/.f64 1 t) (-.f64 z a)))

series59.0ms (1%)

Counts

3 → 144

Calls

3 calls:

29.0ms	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))
19.0ms	(.f64 y (.f64 (/.f64 1 t) (-.f64 z a)))
10.0ms	(*.f64 (/.f64 1 t) (-.f64 z a))

rewrite63.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`distribute-lft-in_binary64`
117×	`distribute-rgt-in_binary64`
92×	`add-sqr-sqrt_binary64`
90×	`prod-diff_binary64`
86×	`*-un-lft-identity_binary64`

Counts

3 → 218

Calls

3 calls:

17.0ms	(.f64 y (.f64 (/.f64 1 t) (-.f64 z a)))
8.0ms	(*.f64 (/.f64 1 t) (-.f64 z a))
7.0ms	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))

simplify147.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

591×	`distribute-rgt-in_binary64`
559×	`distribute-lft-in_binary64`
285×	`associate-r_binary64`
267×	`associate-l_binary64`
221×	`fma-neg_binary64`

Counts

362 → 324

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	5237
1	566	4165
2	1753	3841
3	4844	3841
4	5047	3841

prune220.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	324	7	331

Error

0.0b

Counts

331 → 7

Alt Table

Status	Error	Program
✓	24.1b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	26.9b	(+.f64 x (/.f64 (*.f64 (-.f64 z a) y) t))
	40.3b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
✓	24.7b	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))
	29.7b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
✓	10.4b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	25.3b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))

Compiler

Compiled 7738 to 2975 computations (61.6% saved)

regimes1.0s (18.1%)

Accuracy

Total 6.5b remaining (98.6%)

Threshold costs 0b (0%)

Counts

88 → 3

Compiler

Compiled 9942 to 6006 computations (39.6% saved)

bsearch35.0ms (0.6%)

Steps

Iters	Range		Point
6	1.447359923771939e+154	2.0187932151374388e+155	1.5668554075406726e+154
4	-1.873687390348978e+121	-9.578915754763361e+120	-1.533098449819548e+121

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	53
1	33	53
2	44	53
3	50	53
4	53	53
5	53	53

end92.0ms (1.6%)

Compiler: Compiled 213 to 124 computations (41.8% saved)

Details

analyze1.3s (23.3%)

sample1.5s (26.7%)

simplify130.0ms (2.3%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series74.0ms (1.3%)

rewrite11.0ms (0.2%)

simplify117.0ms (2%)

prune123.0ms (2.1%)

localize10.0ms (0.2%)

series74.0ms (1.3%)

rewrite23.0ms (0.4%)

simplify141.0ms (2.5%)

prune150.0ms (2.6%)

localize7.0ms (0.1%)

series53.0ms (0.9%)

rewrite26.0ms (0.4%)

simplify125.0ms (2.2%)

prune126.0ms (2.2%)

localize8.0ms (0.1%)

series59.0ms (1%)

rewrite63.0ms (1.1%)

simplify147.0ms (2.6%)

prune220.0ms (3.8%)

regimes1.0s (18.1%)

bsearch35.0ms (0.6%)

simplify7.0ms (0.1%)

end92.0ms (1.6%)

Profiling