Details

analyze1.4s (19.1%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (17.6%)

Results

1.1s	8254×	body	128	valid
90.0ms	725×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (1.6%)

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

prune4.0ms (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
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize9.0ms (0.1%)

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)

series59.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
19.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

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

simplify90.0ms (1.3%)

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

prune124.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	1.3b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))) x)
	27.4b	(fma.f64 (/.f64 y a) t x)
	39.9b	(-.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)

Compiler

Compiled 3470 to 1155 computations (66.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series82.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

40.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
22.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
20.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify328.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune285.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	337	6	343

Error

0.0b

Counts

343 → 6

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	0.8b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	27.4b	(fma.f64 (/.f64 y a) t x)
	39.9b	(-.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)))))

Compiler

Compiled 8663 to 2804 computations (67.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.0b	(/.f64 z (-.f64 z t))
✓	0.4b	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
✓	0.8b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)

series274.0ms (3.8%)

Counts

4 → 144

Calls

4 calls:

164.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
82.0ms	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
18.0ms	(/.f64 a (-.f64 z t))
9.0ms	(/.f64 z (-.f64 z t))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
56×	`distribute-lft-out--_binary64`
55×	`add-cube-cbrt_binary64`

Counts

4 → 185

Calls

4 calls:

24.0ms	(/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))
4.0ms	(/.f64 z (-.f64 z t))
4.0ms	(/.f64 a (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)

simplify177.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
309×	`fma-def_binary64`
227×	`+-commutative_binary64`
195×	`associate-/r/_binary64`
182×	`sub-neg_binary64`

Counts

329 → 332

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	804	11377
1	2483	11043
2	5105	11043

prune315.0ms (4.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	333	5	338

Error

0.0b

Counts

338 → 5

Alt Table

Status	Error	Program
	39.9b	(-.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	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 13291 to 5378 computations (59.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
	0.0b	(/.f64 a (-.f64 z t))
	0.0b	(/.f64 z (-.f64 z t))
✓	1.6b	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))

series279.0ms (3.9%)

Counts

2 → 87

Calls

2 calls:

146.0ms	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
133.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))

rewrite96.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

245×	`*-un-lft-identity_binary64`
234×	`times-frac_binary64`
173×	`add-sqr-sqrt_binary64`
84×	`distribute-lft-out--_binary64`
62×	`fma-def_binary64`

Counts

2 → 169

Calls

2 calls:

38.0ms	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
23.0ms	(/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t))))

simplify163.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-/l*_binary64`
562×	`associate-/r*_binary64`
321×	`fma-def_binary64`
193×	`+-commutative_binary64`
169×	`associate-/l/_binary64`

Counts

256 → 285

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	689	10121
1	2015	9638
2	5156	9638

prune371.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	389	2	391
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	391	5	396

Error

Counts

396 → 5

Alt Table

Status	Error	Program
	2.3b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
	32.8b	(fma.f64 (/.f64 1 (+.f64 (sqrt.f64 (/.f64 z (-.f64 z t))) (sqrt.f64 (/.f64 a (-.f64 z t))))) (/.f64 y (-.f64 (sqrt.f64 (/.f64 z (-.f64 z t))) (sqrt.f64 (/.f64 a (-.f64 z t))))) x)
✓	0.8b	(+.f64 (/.f64 y (-.f64 (/.f64 z (-.f64 z t)) (/.f64 a (-.f64 z t)))) x)
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	12.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 15799 to 5321 computations (66.3% saved)

regimes1.5s (21.2%)

Accuracy

Total 1.4b remaining (99.4%)

Threshold costs 0b (0%)

Counts

177 → 1

Compiler

Compiled 28870 to 16158 computations (44% saved)

simplify3.0ms (0%)

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

end72.0ms (1%)

Compiler: Compiled 141 to 75 computations (46.8% saved)

Details

analyze1.4s (19.1%)

sample1.3s (17.6%)

simplify115.0ms (1.6%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series59.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify90.0ms (1.3%)

prune124.0ms (1.7%)

localize9.0ms (0.1%)

series82.0ms (1.2%)

rewrite54.0ms (0.8%)

simplify328.0ms (4.6%)

prune285.0ms (4%)

localize10.0ms (0.1%)

series274.0ms (3.8%)

rewrite56.0ms (0.8%)

simplify177.0ms (2.5%)

prune315.0ms (4.4%)

localize10.0ms (0.1%)

series279.0ms (3.9%)

rewrite96.0ms (1.3%)

simplify163.0ms (2.3%)

prune371.0ms (5.2%)

regimes1.5s (21.2%)

simplify3.0ms (0%)

end72.0ms (1%)

Profiling